Graph details

Graph # 34214

Adjacency matrix

[Too large to display]

Adjacency list

[Too large to display]

HoG graph id

34214

Graph name

Cubic Integral G10

Graph submitted by

Kevin Ryde

Invariant values

The definitions of the invariants can be found here.
Invariant Value Invariant Value
Acyclic No Index 3
Algebraic Connectivity 1 Laplacian Largest Eigenvalue 6
Average Degree 3 Longest Induced Cycle 12
Bipartite Yes Longest Induced Path 13
Chromatic Index 3 Matching Number 10
Chromatic Number 2 Maximum Degree 3
Circumference 20 Minimum Degree 3
Claw-Free No Minimum Dominating Set 6
Clique Number 2 Number of Components 1
Connected Yes Number of Edges 30
Density 0.158 Number of Triangles 0
Diameter 5 Number of Vertices 20
Edge Connectivity 3 Planar No
Eulerian No Radius 4
Genus 2 Regular Yes
Girth 6 Second Largest Eigenvalue 2
Hamiltonian Yes Smallest Eigenvalue -3
Independence Number 10 Vertex Connectivity 3

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

Comments

Posted by Kevin Ryde at Dec 31, 2019 12:36 AM.
This graph is cubic and integral (regular of degree 3 and all roots of the characteristic polynomial of its adjacency matrix are integers). Bussemaker and Cvetković show there are 13 connected cubic integral graphs. This graph is G10 in their numbering of those graphs, and is cospectral with their G9 which is the Desargues graph.

F. C. Bussemaker and D. M. Cvetković, "There Are Exactly 13 Connected, Cubic, Integral Graphs", Publikacije Elektrotehničkog fakulteta, Serija Matematika i fizika, No. 544/576, 1976, pages 43-48, http://www.jstor.org/stable/43667961. Figure 1 graph G10.

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