Cn cycle graph en.wikipedia.org/wiki/Cycle_graph
Kn complete graph en.wikipedia.org/wiki/Complete_graph
Km,n complete bipartite graph en.wikipedia.org/wiki/Complete_bipartite_graph
Pn path graph en.wikipedia.org/wiki/Path_graph
Wn wheel graph en.wikipedia.org/wiki/Wheel_graph


 
N
 
T(N-1)
 
graph #
binary & hex
 
matrix
 
degrees
 
images
 
nicks
 
isomorphic
with
 
 
1
 
0 
1-0
 
[N/A]
 
[N/A]
 
0
 
 
point; hermit; K1
 
1-0
 
 
2
 
1 
2-0
 
0
0x0
 
B
A
0
 
0,0
 
 
two strangers
 
2-0
 
 
2
 
1 
2-1
 
1
0x1
 
B
A
1
 
1,1
 
 
couple; dyad; K2; K1,1
 
2-1
 
 
3
 
3 
3-0
 
000
0x0
 
B
C
A
0
0
B
0
 
0,0,0
 
 
three strangers
 
3-0
 
 
3
 
3 
3-1
 
001
0x1
 
B
C
A
0
0
B
1
 
1,1,0
 
 
three's a crowd, Alice out
 
3-1
 
 
3
 
3 
3-2
 
010
0x2
 
B
C
A
0
1
B
0
 
1,1,0
 
 
three's a crowd, Bob out
 
3-1
 
 
3
 
3 
3-3
 
011
0x3
 
B
C
A
0
1
B
1
 
2,1,1
 
 
everybody knows Carol
 
3-3
 
 
3
 
3 
3-4
 
100
0x4
 
B
C
A
1
0
B
0
 
1,1,0
 
 
three's a crowd, Carol out
 
3-1
 
 
3
 
3 
3-5
 
101
0x5
 
B
C
A
1
0
B
1
 
2,1,1
 
 
everybody knows Bob
 
3-3
 
 
3
 
3 
3-6
 
110
0x6
 
B
C
A
1
1
B
0
 
2,2,1,1TD> 
 
everybody knows Alice
 
3-3
 
 
3
 
3 
3-7
 
111
0x7
 
B
C
A
1
1
B
1
 
2,2,2
 
 
three musketeers; K3; C3
 
3-7
 
 
4
 
6 
4-0
 
000000
0x0
 
B
C
D
A
0
0
0
B
0
0
C
0
 
0,0,0,0
 
 
four strangers
 
4-0
 
 
4
 
6 
4-1
 
000001
0x1
 
B
C
D
A
0
0
0
B
0
0
C
1
 
1,1,0,0
 
 
couple: Carol & Doug
 
4-1
 
 
4
 
6 
4-2
 
000010
0x2
 
B
C
D
A
0
0
0
B
0
1
C
0
 
1,1,0,0
 
 
couple: Bob & Doug
 
4-1
 
 
4
 
6 
4-3
 
000011
0x3
 
B
C
D
A
0
0
0
B
0
1
C
1
 
2,1,1,0
 
 
Doug knows Bob and Carol, not Alice
 
4-3
 
 
4
 
6 
4-4
 
000100
0x4
 
B
C
D
A
0
0
0
B
1
0
C
0
 
1,1,0,0
 
 
couple: Bob and Carol
 
4-1
 
 
4
 
6 
4-5
 
000101
0x5
 
B
C
D
A
0
0
0
B
1
0
C
1
 
2,1,1,0
 
 
Carol knows Bob and Doug, not Alice
 
4-3
 
 
4
 
6 
4-6
 
000110
0x6
 
B
C
D
A
0
0
0
B
1
1
C
0
 
2,1,1,0
 
 
Bob knows Carol and Doug, not Alice
 
4-3
 
 
4
 
6 
4-7
 
000111
0x7
 
B
C
D
A
0
0
0
B
1
1
C
1
 
2,2,2,0
 
 
triangle; clique with Alice excluded
 
4-7
 
 
4
 
6 
4-8
 
001000
0x8
 
B
C
D
A
0
0
1
B
0
0
C
0
 
1,1,0,0
 
 
couple: Alice and Doug
 
4-1
 
 
4
 
6 
4-9
 
001001
0x9
 
B
C
D
A
0
0
1
B
0
0
C
1
 
2,1,1,0
 
 
Doug knows Alice and Carol, not Bob
 
4-3
 
 
4
 
6 
4-10
 
001010
0xA
 
B
C
D
A
0
0
1
B
0
1
C
0
 
2,1,1,0
 
 
Doug knows Alice and Bob, not Carol
 
4-3
 
 
4
 
6 
4-11
 
001011
0xB
 
B
C
D
A
0
0
1
B
0
1
C
1
 
3,1,1,1
 
 
claw; everybody knows Alice
 
4-11
 
 
4
 
6 
4-12
 
001100
0xC
 
B
C
D
A
0
0
1
B
1
0
C
0
 
1,1,1,1
 
 
two couples: Bob & Carol, Alice & Doug
 
4-12
 
 
4
 
6 
4-13
 
001101
0xD
 
B
C
D
A
0
0
1
B
1
0
C
1
 
2,2,1,1
 
 
Carol and Doug are a couple,
plus Carol is friends with Bob and
Doug is friends with Alice; P4
 
4-13
 
 
4
 
6 
4-14
 
001110
0xE
 
B
C
D
A
0
0
1
B
1
1
C
0
 
2,2,1,1
 
 
Bob and Doug are a couple,
plus Bob is friends with Carol and
Doug is friends with Alice; P4
 
4-13
 
 
4
 
6 
4-15
 
001111
0xF
 
B
C
D
A
0
0
1
B
1
1
C
1
 
3,2,2,1
 
 
kite with Doug -> Alice tail
 
4-15
 
 
4
 
6 
4-16
 
010000
0x10
 
B
C
D
A
0
1
0
B
0
0
C
0
 
1,1,0,0
 
 
couple: Alice and Carol
 
4-1
 
 
4
 
6 
4-17
 
010001
0x11
 
B
C
D
A
0
1
0
B
0
0
C
1
 
2,1,1,0
 
 
Carol knows Alice and Doug, not Bob
 
4-3
 
 
4
 
6 
4-18
 
010010
0x12
 
B
C
D
A
0
1
0
B
0
1
C
0
 
1,1,1,1
 
 
two couples: Alice and Carol, Bob and Doug
 
4-12
 
 
4
 
6 
4-19
 
010011
0x13
 
B
C
D
A
0
1
0
B
0
1
C
1
 
2,2,1,1
 
 
Carol and Doug are a couple,
plus Carol is friends with Alice and
Doug is friends with Bob; P4
 
4-13
 
 
4
 
6 
4-20
 
010100
0x14
 
B
C
D
A
0
1
0
B
1
0
C
0
 
2,1,1,0
 
 
Carol knows Alice and Bob, not Doug
 
4-3
 
 
4
 
6 
4-21
 
010101
0x15
 
B
C
D
A
0
1
0
B
1
0
C
1
 
3,1,1,1
 
 
claw; everybody knows Carol
 
4-11
 
 
4
 
6 
4-22
 
010110
0x16
 
B
C
D
A
0
1
0
B
1
1
C
0
 
2,2,1,1
 
 
Bob and Carol are a couple,
plus Bob is friends with Doug and
Carol is friends with Alice; P4
 
4-13
 
 
4
 
6 
4-23
 
010111
0x17
 
B
C
D
A
0
1
0
B
1
1
C
1
 
3,2,2,1
 
 
kite with Carol -> Alice tail
 
4-15
 
 
4
 
6 
4-24
 
011000
0x18
 
B
C
D
A
0
1
1
B
0
0
C
0
 
2,1,1,0
 
 
Alice knows Carol and Doug, not Bob
 
4-3
 
 
4
 
6 
4-25
 
011001
0x19
 
B
C
D
A
0
1
1
B
0
0
C
1
 
2,2,2,0
 
 
triangle; clique with Bob excluded
 
4-7
 
 
4
 
6 
4-26
 
011010
0x1A
 
B
C
D
A
0
1
1
B
0
1
C
0
 
2,2,1,1
 
 
Alice and Doug are a couple,
plus Alice is friends with Carol and
Doug is friends with Bob; P4
 
4-13
 
 
4
 
6 
4-27
 
011011
0x1B
 
B
C
D
A
0
1
1
B
0
1
C
1
 
3,2,2,1
 
 
kite with Doug -> Bob tail
 
4-15
 
 
4
 
6 
4-28
 
011100
0x1C
 
B
C
D
A
0
1
1
B
1
0
C
0
 
2,2,1,1
 
 
Alice and Carol are a couple,
plus Alice is friends with Doug and
Carol is friends with Bob; P4
 
4-13
 
 
4
 
6 
4-29
 
011101
0x1D
 
B
C
D
A
0
1
1
B
1
0
C
1
 
3,2,2,1
 
 
kite with Carol -> Bob tail
 
4-15
 
 
4
 
6 
4-30
 
011110
0x1E
 
B
C
D
A
0
1
1
B
1
1
C
0
 
2,2,2,2
 
 
horizontal bowtie; K2,2; C4
 
4-30
 
 
4
 
6 
4-31
 
011111
0x1F
 
B
C
D
A
0
1
1
B
1
1
C
1
 
3,3,2,2
 
 
everybody knows everybody except Alice and Bob
 
4-31
 
 
4
 
6 
4-32
 
100000
0x20
 
B
C
D
A
1
0
0
B
0
0
C
0
 
1,1,0,0
 
 
couple: Alice and Bob
 
4-1
 
 
4
 
6 
4-33
 
100001
0x21
 
B
C
D
A
1
0
0
B
0
0
C
1
 
1,1,1,1
 
 
two couples: Bob & Carol, Alice & Doug
 
4-12
 
 
4
 
6 
4-34
 
100010
0x22
 
B
C
D
A
1
0
0
B
0
1
C
0
 
2,1,1,0
 
 
Bob knows Alice and Doug, not Carol
 
4-3
 
 
4
 
6 
4-35
 
100011
0x23
 
B
C
D
A
1
0
0
B
0
1
C
1
 
2,2,1,1
 
 
Bob and Doug are a couple,
plus Bob is friends with Alice and
Doug is friends with Carol; P4
 
4-13
 
 
4
 
6 
4-36
 
100100
0x24
 
B
C
D
A
1
0
0
B
1
0
C
0
 
2,1,1,0
 
 
Bob knows Alice and Carol, not Doug
 
4-3
 
 
4
 
6 
4-37
 
100101
0x25
 
B
C
D
A
1
0
0
B
1
0
C
1
 
2,2,1,1
 
 
Bob and Carol are a couple,
plus Bob is friends with Alice and
Carol is friends with Doug; P4
 
4-13
 
 
4
 
6 
4-38
 
100110
0x26
 
B
C
D
A
1
0
0
B
1
1
C
0
 
3,1,1,1
 
 
claw; everybody knows Bob
 
4-11
 
 
4
 
6 
4-39
 
100111
0x27
 
B
C
D
A
1
0
0
B
1
1
C
1
 
3,2,2,1
 
 
kite with Bob -> Alice tail
 
4-15
 
 
4
 
6 
4-40
 
101000
0x28
 
B
C
D
A
1
0
1
B
0
0
C
0
 
2,1,1,0
 
 
Alice knows Bob and Doug, not Carol
 
4-3
 
 
4
 
6 
4-41
 
101001
0x29
 
B
C
D
A
1
0
1
B
0
0
C
1
 
2,2,1,1
 
 
Alice and Doug are a couple,
plus Alice is friends with Bob and
Doug is friends with Carol; P4
 
4-13
 
 
4
 
6 
4-42
 
101010
0x2A
 
B
C
D
A
1
0
1
B
0
1
C
0
 
2,2,2,0
 
 
triangle; clique with Carol excluded
 
4-7
 
 
4
 
6 
4-43
 
101011
0x2B
 
B
C
D
A
1
0
1
B
0
1
C
1
 
3,2,2,1
 
 
kite with Doug -> Carol tail
 
4-15
 
 
4
 
6 
4-44
 
101100
0x2C
 
B
C
D
A
1
0
1
B
1
0
C
0
 
2,2,1,1
 
 
Alice and Doug are a couple,
plus Alice is friends with Bob and
Doug is friends with Carol; P4
 
4-13
 
 
4
 
6 
4-45
 
101101
0x2D
 
B
C
D
A
1
0
1
B
1
0
C
1
 
2,2,2,2
 
 
vertical bowtie; K2,2; C4
 
4-30
 
 
4
 
6 
4-46
 
101110
0x2E
 
B
C
D
A
1
0
1
B
1
1
C
0
 
3,2,2,1
 
 
kite with Bob -> Carol tail
 
4-15
 
 
4
 
6 
4-47
 
101111
0x2F
 
B
C
D
A
1
0
1
B
1
1
C
1
 
3,3,2,2
 
 
everybody knows everybody except Alice and Carol
 
4-31
 
 
4
 
6 
4-48
 
110000
0x30
 
B
C
D
A
1
1
0
B
0
0
C
0
 
2,1,1,0
 
 
Alice knows Bob and Carol, not Doug
 
4-3
 
 
4
 
6 
4-49
 
110001
0x31
 
B
C
D
A
1
1
0
B
0
0
C
1
 
2,2,1,1
 
 
Alice and Carol are a couple,
plus Alice is friends with Bob and
Carol is friends with Doug; P4
 
4-13
 
 
4
 
6 
4-50
 
110010
0x32
 
B
C
D
A
1
1
0
B
0
1
C
0
 
2,2,1,1
 
 
Alice and Bob are a couple,
plus Alice is friends with Carol and
Bob is friends with Doug; P4
 
4-13
 
 
4
 
6 
4-51
 
110011
0x33
 
B
C
D
A
1
1
0
B
0
1
C
1
 
2,2,2,2
 
 
box; K2,2; C4
 
4-30
 
 
4
 
6 
4-52
 
110100
0x34
 
B
C
D
A
1
1
0
B
1
0
C
0
 
2,2,2,0
 
 
triangle; clique with Doug excluded
 
4-7
 
 
4
 
6 
4-53
 
110101
0x35
 
B
C
D
A
1
1
0
B
1
0
C
1
 
3,2,2,1
 
 
kite with Carol -> Doug tail
 
4-15
 
 
4
 
6 
4-54
 
110110
0x36
 
B
C
D
A
_
_
_
B
_
_
C
_
 
3,2,2,1
 
 
kite with Bob -> Doug tail
 
4-15
 
 
4
 
6 
4-55
 
110111
0x37
 
B
C
D
A
1
1
0
B
1
1
C
1
 
3,3,2,2
 
 
everybody knows everybody except Alice and Doug
 
4-31
 
 
4
 
6 
4-56
 
111000
0x38
 
B
C
D
A
1
1
1
B
0
0
C
0
 
3,1,1,1
 
 
claw; everybody knows Alice
 
4-11
 
 
4
 
6 
4-57
 
111001
0x39
 
B
C
D
A
1
1
1
B
0
0
C
1
 
3,2,2,1
 
 
kite with Alice -> Bob tail
 
4-15
 
 
4
 
6 
4-58
 
111010
0x3A
 
B
C
D
A
1
1
1
B
0
1
C
0
 
3,2,2,1
 
 
kite with Alice -> Carol tail
 
4-15
 
 
4
 
6 
4-59
 
111011
0x3B
 
B
C
D
A
1
1
1
B
0
1
C
1
 
3,3,2,2
 
 
everybody knows everybody except Bob and Carol
 
4-31
 
 
4
 
6 
4-60
 
111100
0x3C
 
B
C
D
A
1
1
1
B
1
0
C
0
 
3,2,2,1
 
 
kite with Alice -> Doug tail
 
4-15
 
 
4
 
6 
4-61
 
111101
0x3D
 
B
C
D
A
1
1
1
B
1
0
C
1
 
3,3,2,2
 
 
everybody knows everybody except Bob and Doug
 
4-31
 
 
4
 
6 
4-62
 
111110
0x3E
 
B
C
D
A
1
1
1
B
1
1
C
0
 
3,3,2,2
 
 
everybody knows everybody except Carol and Doug
 
4-31
 
 
4
 
6 
4-63
 
111111
0x3F
 
B
C
D
A
1
1
1
B
1
1
C
1
 
3,3,3,3
 
 
K4; W4
 
4-63