Graph details

Graph # 45597

Adjacency matrix

011110000000000
100010011000000
100100000110000
101000000000110
110000000001001
000000010100011
000000001011100
010001001100000
010000110000100
001001010010000
001000100101000
000010100010001
000100101000010
000101000000101
000011000001010

Adjacency list

1: 2 3 4 5
2: 1 5 8 9
3: 1 4 10 11
4: 1 3 13 14
5: 1 2 12 15
6: 8 10 14 15
7: 9 11 12 13
8: 2 6 9 10
9: 2 7 8 13
10: 3 6 8 11
11: 3 7 10 12
12: 5 7 11 15
13: 4 7 9 14
14: 4 6 13 15
15: 5 6 12 14

HoG graph id

45597

Graph name

Line graph of Petersen Graph

Graph submitted by

Krystal Guo

Invariant values

The definitions of the invariants can be found here.
Invariant Value Invariant Value
Acyclic No Index 4
Algebraic Connectivity 2 Laplacian Largest Eigenvalue 6
Average Degree 4 Longest Induced Cycle 9
Bipartite No Longest Induced Path 8
Chromatic Index 5 Matching Number 7
Chromatic Number 4 Maximum Degree 4
Circumference 15 Minimum Degree 4
Claw-Free Yes Minimum Dominating Set 3
Clique Number 3 Number of Components 1
Connected Yes Number of Edges 30
Density 0.286 Number of Triangles 10
Diameter 3 Number of Vertices 15
Edge Connectivity 4 Planar No
Eulerian Yes Radius 3
Genus 1 Regular Yes
Girth 3 Second Largest Eigenvalue 2
Hamiltonian Yes Smallest Eigenvalue -2
Independence Number 5 Vertex Connectivity 4

A table row rendered like this indicates that the graph is marked as being interesting for that invariant.

Comments

Posted by Krystal Guo at Mar 31, 2021 6:08 PM.
This is the point graph of the generalized quadrangle (2,2) with the edges of a spread deleted. It is a diameter 3, antipodal, distance-regular graph with intersection array {4,2,1;1,1,4}. It is also the line graph of the Petersen Graph. It is distance-transitive and the automorphism graph is Sym(5), the symmetric group on 5 elements. See https://www.distanceregular.org/graphs/line-petersen.html

Embeddable in the projective plane with 10 faces of degree 3 and 6 faces of degree 5.

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