Contents
Graphs ordered alphabetically
Note that complements are usually not listed. So for e.g. co-fork,
look for fork. The X... names are by ISGCI, the other names are from the literature.
- 2-fan
- 2C4
- 2K1
- 2K2
- 2K3
- 2K3 + e
- 2P3
- 2diamond
- 3-fan
- 3-pan
- 3K1
- 3K2
- 4-fan
- 4-pan
- 4K1
- 5-pan
- 5K1
- 5K1 + e
- 6-fan
- 6-pan
- A
- A ∪ K1
- BW3
- BW4
- C(n,k)
- C3
- C4
- C4 ∪ 2K1
- C4 ∪ K1
- C4 ∪ P2
- C5
- C5 ∪ K1
- C6
- C7
- C7 ∪ K1
- C8
- Cn
- E
- G ∪ N
- G+e
- G-e
- H
- K2
- K2 ∪ 3K1
- K2 ∪ K3
- K2 ∪ K1,3
- K2 ∪ claw
- K3
- K3 ∪ 2K1
- K3 ∪ 3K1
- K3 ∪ P3
- K4
- K4 - e
- K4 ∪ K1
- K5
- K5 - e
- Kn
- K1,3
- K1,4
- K1,4+e
- K2,2
- K2,3
- K3,3
- K3,3 ∪ K1
- K3,3+e
- K3,3-e
- Kn,m
- L(K3,3)
- P
- P2 ∪ P3
- P2 ∪ P4
- P3
- P3 ∪ 2K1
- P3 ∪ P4
- P3 ∪ P3
- P4
- P5
- P6
- P7
- Pn
- R
- S3
- 2P3 ∪ K1
- P ∪ K1
- X35 ∪ K1
- antenna
- anti-hole
- apple
- banner
- biclique
- bicycle
- building
- bull
- butterfly
- butterfly ∪ K1
- cap
- chair
- claw
- claw ∪ 3K1
- claw ∪ K1
- claw ∪ triangle
- clique wheel
- co-fork ∪ K1
- complete bipartite graph
- complete graph
- complete sun
- cricket
- cross
- cycle
- dart
- diamond
- diamond ∪ K1
- domino
- eiffeltower
- even building
- even-cycle
- even-hole
- fan
- fish
- fork
- gem
- gem ∪ K1
- hole
- hourglass
- house
- jewel
- kite
- kite ∪ K1
- longhorn
- n-fan
- n-pan
- nG
- net
- net ∪ K1
- odd anti-hole
- odd building
- odd-cycle
- odd-hole
- odd-sun
- pan
- parachute
- parapluie
- path
- paw
- rising sun
- skew-star
- spideri,j,k
- star
- star1,1,1,2
- star1,1,3
- star1,1,3 ∪ K1
- star1,2,2
- star1,2,3
- star2,2,2
- stari,j,k
- sun
- sunlet4
- triad
- triangle
- twin-C5
- twin-house
- twin3-house
- wheel
Graphs ordered by number of vertices
2 vertices
- Graphs are ordered by increasing number
of edges in the left column.
The list contains all
2
graphs with 2 vertices.
2K1A?
K2A_
3 vertices
- Graphs are ordered by increasing number
of edges in the left column.
The list contains all
4
graphs with 3 vertices.
3K1
= co-triangleB?
triangle
= K3
= C3Bw
P3BO
P3Bg
4 vertices
- Graphs are ordered by increasing number
of edges in the left column.
The list contains all
11
graphs with 4 vertices.
4K1
= K4C?
K4
= W3C~
co-diamondCC
diamond
= K4 - e
= 2-fanCz
co-pawCE
paw
= 3-panCx
2K2
= C4CK
C4
= K2,2Cr
claw
= K1,3Cs
co-clawCJ
P4Ch
5 vertices
- Graphs are ordered by increasing number
of edges in the left column.
The list contains all
34
graphs with 5 vertices.
5K1
= K5D??
K5D~{
K5 - e
= 5K1 + e
= K2 ∪ 3K1D?O
K5 - eD~k
P3 ∪ 2K1Do?
P3 ∪ 2K1DN{
W4DQ?
W4Dl{
claw ∪ K1Ds?
claw ∪ K1DJ{
P2 ∪ P3D`C
P2 ∪ P3D]w
co-gemDU?
gem
= 3-fanDh{
K3 ∪ 2K1Dw?
K3 ∪ 2K1DF{
K1,4Ds_
K1,4
= K4 ∪ K1DJ[
co-butterfly
= C4 ∪ K1DBW
butterfly
= hourglassD{c
fork
= chairDiC
co-fork
= kite
= co-chair
= chairDTw
co-dartDGw
dartDvC
P5DhC
house
= P5DUw
K2 ∪ K3
= K2,3D`K
K2,3D]o
P
= 4-pan
= bannerDrG
PDKs
bullD{O
cricket
= K1,4+eDiS
co-cricket
= diamond ∪ K1DTg
C5Dhc
6 vertices
- Graphs are ordered by increasing number
of edges in the left column.
The list does not contain all
graphs with 6 vertices.
3K2E`?G
3K2E]~o
X197
= P3 ∪ P3EgC?
X197EVzw
K3 ∪ 3K1Ew??
K3 ∪ 3K1
= jewelEF~w
P2 ∪ P4Eh?G
P2 ∪ P4EU~o
2P3EgCG
2P3EVzo
C4 ∪ 2K1El??
C4 ∪ 2K1EQ~w
K2 ∪ claw
= K2 ∪ K1,3Es?G
K2 ∪ clawEJ~o
cross
= star1,1,1,2EiD?
co-crossETyw
HEgSG
HEVjo
C4 ∪ P2El?G
C4 ∪ P2EQ~o
E
= star1,2,2EhC_
E
= co-star1,2,2EUzW
K3 ∪ P3EWCW
K3,3+eEfz_
X198
= P ∪ K1EhK?
X198EUrw
P6EhCG
P6EUzo
W5
= C5 ∪ K1EUW?
W5Ehfw
X172
= star1,1,3EhCO
X172EUzg
co-fork ∪ K1
= kite ∪ K1EDaW
co-fork ∪ K1
= kite ∪ K1Ey\_
butterfly ∪ K1E{c?
butterfly ∪ K1EBZw
co-4-fanEUw?
4-fanEhFw
AEhSG
AEUjo
RElCO
REQzg
2K3
= K3,3EwCW
K3,3EFz_
C6EhEG
C6EUxo
X98EQUO
X98
= twin3-houseElhg
net
= S3EDbO
S3Ey[g
X18ElCG
X18EQzo
5-panEhcG
5-panEUZo
X166EhD_
X166EUyW
X169EhGg
X169EUvO
X84ElD?
X84EQyw
X95EXCW
X95Eez_
gem ∪ K1Eq{?
gem ∪ K1ELBw
W4 ∪ K1EQBw
W4 ∪ K1El{?
X37EhMG
X37EUpo
fishErCW
co-fishEKz_
dominoErGW
co-dominoEKv_
twin-C5EhdG
co-twin-C5
= twin-C5EUYo
X58EUwG
X58EhFo
2K3 + e
= K3,3-eEwCw
K3,3-eEFz?
X5EAxo
X5E|EG
antennaEjCg
co-antennaESzO
X45EhQg
X45EUlO
co-twin-house
= twin-houseEQKw
twin-houseElr?
X167EhTO
X167EUig
X168EhPo
X168EUmG
X170EhGw
X170EUv?
X171EhCw
X171EUz?
X96EgTg
X96EViO
X163Ehp_
X163EUMW
7 vertices
- Graphs are ordered by increasing number
of edges in the left column.
The list does not contain all
graphs with 7 vertices.
claw ∪ 3K1Fs???
claw ∪ 3K1FJ~~w
P3 ∪ P4Fh?GG
P3 ∪ P4FU~vo
X177
= star1,1,3 ∪ K1FhCO?
X177FUznw
A ∪ K1Fr?__
A ∪ K1FK~^W
net ∪ K1FjGO?
net ∪ K1FSvnw
T2
= star2,2,2FhC_G
T2FUz^o
P7FhCGG
P7FUzvo
star1,2,3
= skew-starFhCG_
star1,2,3FUzvW
X85FhD?_
X85FUy~W
claw ∪ triangleFs?GW
claw ∪ triangleFJ~v_
6-panFhEGG
6-panFUxvo
C7FhCKG
C7FUzro
X12FKdE?
X12FrYxw
X41FhO_W
X41FUn^_
longhornFhCH_
co-longhornFUzuW
X2FhDOG
X2FUyno
X6Fl_GO
X6FQ^vg
X130FhDAG
X130FUy|o
eiffeltowerFhCoG
co-eiffeltowerFUzNo
X11FKde?
X11FrYXw
X20FhCiG
X20FUzTo
X38FhCKg
X38FUzrO
X3FrGX?
X3FKvew
X7Fl_GW
X7FQ^v_
X27FlGHG
X27FQvuo
X30FhOgW
X30FUnV_
X173FhEKG
X173FUxro
X175FUwK?
X175FhFrw
X90FUWPG
X90Fhfmo
X106FSwq?
X106FjFLw
X127F`GV_
X127F]vgW
X128FUg`G
X128FhV]o
X134FhDWG
X134FUyfo
X162FsiOG
X162FJTno
K3,3 ∪ K1FFz_?
K3,3 ∪ K1FwC^w
S3 ∪ K1Fy[g?
S3 ∪ K1FDbVw
X42FExaO
X42FxE\g
X32FhFh?
X32FUwUw
X9FhEhO
X9FUxUg
X8FrGWW
X8FKvf_
X33FhEj?
X33FUxSw
co-rising sunF?M]W
rising sunF~p`_
X39FhhOW
X39FUUn_
X46FUhS_
X46FhUjW
X15FQFb_
X15Flw[W
W6FLv_?
W6FqG^w
BW3FqG[o
BW3FLvbG
parapluie
= co-parachuteFAYFo
parachute
= co-parapluieF|dwG
X82FGrEg
X82FvKxO
X176FhCJo
X176FUzsG
X87FUYT?
X87Fhdiw
X88FDbRO
X88Fy[kg
X89FUWsG
X89FhfJo
X92FErF?
X92FxKww
X97F?vFO
X97F~Gwg
X184F_Kz_
X184F^rCW
X103FEPqg
X103FxmLO
X105FUwo_
X105FhFNW
X129FhCeo
X129FUzXG
X132FhDEg
X132FUyxO
X159FsioG
X159FJTNo
X199FhCNo
X199FUzoG
co-6-fanFUzo?
6-fanFhCNw
X200FUxoG
X200FhENo
X13FlwWG
X13FQFfo
X36FhhWW
X36FUUf_
X35FhFj?
X35FUwSw
X70FuwGW
X70FHFv_
X14FQFf_
X14FlwWW
X34FDauo
X34Fy\HG
X40FhhoW
X40FUUN_
X1FDa]o
X1Fy\`G
X10FrGXW
X10FKve_
X17FKzc_
X17FrCZW
X31FhFx?
X31FUwEw
X86FUWZG
X86Fhfco
X93FErf?
X93FxKWw
X99FFzc?
X99FwCZw
X100FgCNw
X100
= 2P3 ∪ K1FVzo?
X101FwC\g
X101FFzaO
X102FgC^g
X102FVz_O
X104FxELO
co-X104FExqg
X107FUPqg
X107FhmLO
X133FU@]W
X133Fh}`_
8 vertices
- Graphs are ordered by increasing number
of edges in the left column.
The list does not contain all
graphs with 8 vertices.
X108
= C7 ∪ K1GhCKG?
X108GUzrv{
2C4Gl?GGS
2C4GQ~vvg
X19GhCI@C
X19GUzt}w
sunlet4Gl`@?_
sunlet4GQ]}~[
C8GhCGKC
C8GUzvrw
X71GiGWGO
X71GTvfvk
X77GxEG_G
X77GExv^s
X165Gl`H?_
X165GQ]u~[
X152GO?O~C
X152Gn~n?w
X205GrGX?S
X205GKve~g
X74G?pk`c
X74G~MR]W
X180
= 2diamondG|?GWS
X180GA~vfg
X164Gl`H?c
X164GQ]u~W
X29G?bFF_
X29G~[ww[
X117Gk?Xoc
X117GR~eNW
X125
= X35 ∪ K1GGGqHw
X125GvvLuC
X204G|?GYS
X204GA~vdg
X22GhSIhC
X22GUjtUw
X26GkQAhS
X26GRl|Ug
X25GDhXGo
X25GyUevK
X181G|GGWS
X181GAvvfg
X182Gh{GGK
X182GUBvvo
X110
= X35 ∪ K1GBTHqC
X110G{iuLw
X114GgGsHw
X114GVvJuC
X116GgKkpC
X116GVrRMw
X53GUxQS_
X53GhElj[
X28GlUad?
X28GQh\Y{
X185GhRHhC
X185GUkuUw
X188GQLTUG
X188Glqihs
X79GhELQg
X79GUxqlS
X111GhKMKg
X111GUrprS
X115GkGohw
X115GRvNUC
X119G@zsT?
X119G}CJi{
X124GRTKqC
X124GkirLw
X126GSW]J_
X126Gjf`s[
X131GJEw[_
X131GsxFb[
X142Gl_fa_
X142GQ^W\[
X150GQMWD[
X150Glpfy_
X52GUxQU_
X52GhElh[
X80GhELQk
X80GUxqlO
X47GhEhhW
X47GUxUUc
X48GhElHW
X48GUxQuc
X178GnfB@_
X178GOW{}[
X187GQLTUW
X187Glqihc
X189GhdWJS
X189GUYfsg
X192GUWmdG
X192GhfPYs
X193GUXPQ[
X193Gheml_
X109GhCMLw
X109GUzpqC
X118G[bpoc
X118Gb[MNW
X120GUrpb?
X120GhKM[{
X121GxKJKg
X121GErsrS
X123Gbe@s[
X123G[X}J_
X135GHPjn?
X135GumSO{
X137GEmSO{
X137GxPjn?
X143Gl_fq_
X143GQ^WL[
X144Gl`fa_
X144GQ]W\[
X149GQMWL[
X149Glpfq_
X151GQ]WD[
X151Gl`fy_
X161GSiSFw
X161GjTjwC
X50GhEhh[
X50GUxUU_
X51GhElH[
X51GUxQu_
X49GhElhW
X49GUxQUc
S4G~fB@_
X186Ghqihc
X190GVWs]G
X190GgfJ`s
X191GhfPYS
X191GUWmdg
X83GjbiJC
X83GS[Tsw
X112GjCMNW
X112GSzpoc
X113GxCJLw
X113GEzsqC
X122G{guHo
X122GBVHuK
X136GXPjn?
X136GemSO{
X145Glpfa_
X145GQMW\[
X146Gl`fi_
X146GQ]WT[
X147Gh`fy_
X147GU]WD[
X148Gl`fq_
X148GQ]WL[
X160GjTJwC
9 vertices
- Graphs are ordered by increasing number
of edges in the left column.
The list does not contain all
graphs with 9 vertices.
X94HgSG?S@
X94HVjv~j}
X207HhCGHO@
X207HUzvun}
X91HgCg?Cd
X91HVzV~zY
X73HhEI?_C
X73HUxt~^z
X43HhD@GcA
X43HUy}vZ|
X21HhSIgC_
X21HUjtVz^
X138HQr?OJK
X138HlK~nsr
X24HLCgLS@
X24HqzVqj}
BW4HhCGKEi
BW4HUzvrxT
X139HQr?OJk
X139HlK~nsR
X141HQR?OJm
X141Hlk~nsP
X23HhSIkCa
X23HUjtRz\
X140HQr?OJm
X140HlK~nsP
X179H{OebQc
X179HBnX[lZ
X154HO?O~Mr
X154Hn~n?pK
X56HUxQScB
X56HhEljZ{
X153HO?O~Nr
X153Hn~n?oK
X201H~|_{A?
X201H?A^B|~
X55HUxQScZ
X55HhEljZc
X54HUxQSdJ
X54HhEljYs
X202
= L(K3,3)H{S{aSf
10 vertices
- Graphs are ordered by increasing number
of edges in the left column.
The list does not contain all
graphs with 10 vertices.
X81IkCOK?@A?
T3IhCGG_@?G
X75IhEI@?CA?
X75IUxt}~z|w
X44IhCH?cA?W
X76IhEI@CCAG
X76IUxt}zz|o
X206IhCGLOi?W
X206IUzvqnT~_
X183IgCNwC@?W
X183IVzoFz}~_
X174IheAHCPBG
X174IUX|uzm{o
X72IheMB?oE?
X72IUXp{~Nxw
X4IhEFHCxAG
X4IUxwuzE|o
X194IAzpsX_WG
X194I|CMJe^fo
X195IzKWWMBoW
X195ICrffp{N_
X155In~mB?WB?
X155IO?P{~f{w
X156In~mB?WR?
X156IO?P{~fkw
X157IO?Pk~fkw
X157In~mR?WR?
X158In|mR?WR?
X158IOAPk~fkw
11 vertices
- Graphs are ordered by increasing number
of edges in the left column.
The list does not contain all
graphs with 11 vertices.
X59JhC?GC@?HA?
X208JhCGH?GCW_?
X57JhEljXz{@y_
13 vertices
- Graphs are ordered by increasing number
of edges in the left column.
The list does not contain all
graphs with 13 vertices.
X203LhEH?C@CG?_@A@
X196L~[ww[F?{BwFwF
X196L?bFFbw~B{FwFw
Configurations XC
A configuration XC represents a family of graphs by specifying
edges that must be present (solid lines), edges that must not be
present (dotted lines), and edges that may or may not be present (not
drawn). For example,
XC1 represents
W4,
gem.
XC1
XC2
XC3
XC4
XC5
XC6
XC7
XC8
XC9
XC10
XC11
XC12
XC13
Configurations XZ
A configuration XZ represents a family of graphs by specifying
edges that must be present (solid lines), edges that must not be
present (not drawn), and edges that may or may not be present (red
dotted lines).
XZ1
XZ2
XZ3
XZ4
XZ5
XZ6
XZ7
XZ8
XZ9
XZ10
XZ11
XZ12
XZ13
XZ14
XZ15
Families XF
Families are normally specified as
XFif(n) where n implicitly
starts from 0. For example, XF12n+3 is
the set XF13, XF15,
XF17...
XF1n
XF1n (n >= 0) consists of a
path P of
lenth n and a vertex that is adjacent to every vertex of P.
To both endpoints of P a pendant vertex is attached. Examples:
XF10 = claw ,
XF11 = bull .
XF13 = X176 .
XF2n
XF2n (n >= 0) consists of a
path P of
length n and a vertex u that is adjacent to every vertex of
P. To both endpoints of P, and to u a pendant vertex
is attached. Examples:
XF20 = fork ,
XF21 = net .
XF3n
XF3n (n >= 0) consists of a
path
P=p1 ,..., pn+1 of length n, a
triangle abc and two vertices u,v. a and c
are adjacent to every vertex of P, u is adjacent to
a,p1 and v is adjacent to
c,pn+1. Examples:
XF30 = S3 ,
XF31 = rising sun .
XF4n
XF4n (n >= 0) consists of a
path
P=p1 ,..., pn+1 of length n, a
P3 abc and two vertices u,v. a and
c are adjacent to every vertex of P, u is adjacent
to a,p1 and v is adjacent to
c,pn+1. Examples:
XF40 = co-antenna ,
XF41 = X35 .
XF5n
XF5n (n >= 0) consists of a
path
P=p1 ,..., pn+1 of length n, and four
vertices a,b,u,v. a and b are adjacent to every
vertex of P, u is adjacent to a,p1 and
v is adjacent to b,pn+1.
Examples:
XF50 = butterfly ,
XF51 = A .
XF52 = X42 .
XF53 = X47 .
XF6n
XF6n (n >= 0) consists of a
path
P=p1 ,..., pn+1 of length n, a
P2 ab and two vertices u,v. a and
b are adjacent to every vertex of P, u is adjacent
to a,p1 and v is adjacent to
b,pn+1.
Examples:
XF60 = gem ,
XF61 = H ,
XF62 = X175 .
XF7n
XF7n (n >= 2) consists of n independent
vertices v1 ,..., vn and n-1
independent vertices w1 ,..., wn-1.
wi is adjacent to vi and to
vi+1. A vertex a is adjacent to all
vi. A pendant edge is attached to a, v1 ,
vn.
XF8n
XF8n (n >= 2)
consists of n independent vertices v1 ,...,
vn ,n-1 independent vertices
w1 ,..., wn-1,
and a P3 abc.
wi is adjacent to
vi and to vi+1.
a is adjacent to v1 ,...,
vn-1, c is adjacent to
v2,...vn.
A pendant vertex is attached to b.
XF9n
XF9n (n>=2)
consists of a P2n
p1 ,..., p2n
and a C4 abcd. pi
is adjacent to a when i is odd, and to b when
i is even.
A pendant vertex is attached to p1 and
to p2n.
XF10n
XF10n (n >= 2)
consists of a Pn+2 a0 ,..., an+1,
a Pn+2 b0 ,..., bn+1 which are
connected by edges (a1, b1) ...
(an, bn).
XF11n
XF11n (n >= 2)
consists of a Pn+1 a0 ,..., an,
a Pn+1 b0 ,..., bn and a
P2 cd. The following edges are added:
(a1, b1) ... (an,
bn),
(c, an) ... (c, bn).
General families
C(n,k)
with n,k relatively prime and n > 2k consists of vertices
a0,..,an-1 and b0,..,bn-1.
ai is adjacent to aj with j-i <= k (mod n);
bi is adjacent to bj with j-i < k (mod n); and
ai is adjacent to bj with j-i <= k (mod n). In
other words, ai is adjacent to
ai-k..ai+k, and to
bi-k,..bi+k-1 and bi is adjacent to
ai-k+1..ai+k and to
bi-k+1..bi+k-1.
Example:
C(3,1) = S3 ,
C(4,1) = X53 ,
C(5,1) = X72 .
G ∪ N
is the disjoint union of G and N.
G+e
is formed from a graph G by adding an edge between two arbitrary
unconnected nodes. Example: cricket .
G-e
is formed from a graph G by removing an arbitrary edge.
Example:
K5 - e ,
K3,3-e .
anti-hole
is the complement of a hole . Example:
C5 .
apple
are the (n+4)-pan s.
biclique
= Kn,m
= complete bipartite graph
consist of a non-empty independent set U of n vertices, and a non-empty independent
set W of m vertices and have an edge (v,w) whenever v in U and w
in W. Example: claw ,
K1,4 ,
K3,3 .
bicycle
consists of two cycle s C and D, both of length 3
or 4, and a path P. One
endpoint of P is identified with a vertex of C and the other
endpoint is identified with a vertex of D. If both C and D are
triangles, than P must have at least 2 edges, otherwise P may have
length 0 or 1. Example:
fish ,
X7 ,
X11 ,
X27 .
building
= cap
is created from a hole by adding a single chord
that forms a triangle with two edges of the hole
(i.e. a single chord that is a short chord). Example:
house .
clique wheel
consists of a clique V={v0,..,vn-1}
(n>=3) and two independent sets P={p0,..pn-1}
and Q={q0,..qn-1}.
pi is adjacent to all vj
such that j != i (mod n). qi is adjacent to all
vj such that j != i-1, j != i (mod n).
pi is adjacent to qi.
Example: X179 .
complete graph
= Kn
have n nodes and an edge between every pair (v,w) of vertices with v
!= w. Example: triangle ,
K4 .
complete sun
is a sun for which U is a complete graph.
Example: S3 ,
S4 .
cycle
= Cn
have nodes 0..n-1 and edges (i,i+1 mod n) for 0<=i<=n-1.
Example:
triangle ,
C4 ,
C5 ,
C6 ,
C8
even building
is a building with an even number of vertices.
Example: X37 .
even-cycle
is a cycle with an even number of nodes.
Example:
C4 , C6 .
even-hole
is a hole with an even number of nodes. Example:
C6 , C8 .
fan
= n-fan
are formed from a Pn+1 (that is, a
path of length n) by adding a
vertex that is adjacent to every vertex of the path. Example:
diamond ,
gem ,
4-fan .
hole
is a cycle with at least 5 nodes. Example:
C5 .
nG
consists of n disjoint copies of G.
odd anti-hole
is the complement of an odd-hole . Example:
C5 .
odd building
is a building with an odd number of vertices.
Example: house .
odd-hole
is a hole with an odd number of nodes. Example:
C5 .
odd-sun
is a sun for which n is odd.
Example: S3 .
pan
= n-pan
is formed from the cycle Cn
adding a vertex which is adjacent to precisely one vertex of the cycle.
Example:
paw ,
4-pan ,
5-pan ,
6-pan .
path
= Pn
have nodes 1..n and edges (i,i+1) for 1<=i<=n-1. The length of
the path is the number of edges (n-1). Example:
P3 ,
P4 ,
P5 ,
P6 ,
P7 .
stari,j,k
= triad
= spideri,j,k
are trees with 3 leaves that are connected to a single vertex of
degree three with paths of length i, j, k, respectively. Example:
star1,2,2 ,
star1,2,3 ,
fork ,
claw .
The generalisation to an unspecified number of leaves are known as
spiders.
sun
A sun is a chordal graph on 2n nodes (n>=3) whose vertex set can
be partitioned into W = {w1..wn}
and U = {u1..un}
such that W is independent and ui is adjacent
to wj iff i=j or i=j+1 (mod n).
Example: S3 ,
S4 .
wheel
= Wn
is formed from the cycle Cn
adding a vertex which is adjacent to every vertex of the cycle. Example:
K4 ,
W4 ,
W5 ,
W6 .