Graph details

Graph # 45595

Adjacency matrix

01110000
10001100
10010010
10100001
01000011
01000011
00101100
00011100

Adjacency list

1: 2 3 4
2: 1 5 6
3: 1 4 7
4: 1 3 8
5: 2 7 8
6: 2 7 8
7: 3 5 6
8: 4 5 6

HoG graph id

45595

Graph name

n/a

Graph submitted by

House of Graphs

Invariant values

The definitions of the invariants can be found here.
Invariant Value Invariant Value
Acyclic No Index 3
Algebraic Connectivity 1.438 Laplacian Largest Eigenvalue 5.562
Average Degree 3 Longest Induced Cycle 5
Bipartite No Longest Induced Path 4
Chromatic Index 3 Matching Number 4
Chromatic Number 3 Maximum Degree 3
Circumference 8 Minimum Degree 3
Claw-Free No Minimum Dominating Set 3
Clique Number 3 Number of Components 1
Connected Yes Number of Edges 12
Density 0.429 Number of Triangles 1
Diameter 2 Number of Vertices 8
Edge Connectivity 3 Planar No
Eulerian No Radius 2
Genus 1 Regular Yes
Girth 3 Second Largest Eigenvalue 1.562
Hamiltonian Yes Smallest Eigenvalue -2.562
Independence Number 3 Vertex Connectivity 3

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

Comments

Posted by House of Graphs at Mar 30, 2021 9:08 PM.
A cubic graph with the maximum number of edge-Kempe equivalence classes for the given order. See: "J. Goedgebeur and P.R.J. Ostergard, Switching 3-edge-colorings of cubic graphs, manuscript, 2021" for more details.

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