Graph details

Graph # 1022

Adjacency matrix

01110000
10000110
10000101
10000011
00000111
01101000
01011000
00111000

Adjacency list

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

HoG graph id

1022

Graph name

Cubical Graph

Graph submitted by

MathWorld

Invariant values

The definitions of the invariants can be found here.
Invariant Value Invariant Value
Acyclic No Index 3
Algebraic Connectivity 2 Laplacian Largest Eigenvalue 6
Average Degree 3 Longest Induced Cycle 6
Bipartite Yes Longest Induced Path 4
Chromatic Index 3 Matching Number 4
Chromatic Number 2 Maximum Degree 3
Circumference 8 Minimum Degree 3
Claw-Free No Minimum Dominating Set 2
Clique Number 2 Number of Components 1
Connected Yes Number of Edges 12
Density 0.429 Number of Triangles 0
Diameter 3 Number of Vertices 8
Edge Connectivity 3 Planar Yes
Eulerian No Radius 3
Genus 0 Regular Yes
Girth 4 Second Largest Eigenvalue 1
Hamiltonian Yes Smallest Eigenvalue -3
Independence Number 4 Vertex Connectivity 3

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

Comments

Posted by MathWorld at Mar 28, 2012 11:57 AM.
Source: MathWorld and GraphData in Mathematica.

Posted by House of Graphs at Jan 29, 2019 9:24 AM.
A connected integral graph. A graph is called integral if all of its eigenvalues of its adjacency matrix are integral. See "Krzysztof T. ZwierzyƄski, Generating Integral Graphs Using PRACE Research Infrastructure" for more information.

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