Graph details

Graph # 45683

Adjacency matrix

[Too large to display]

Adjacency list

[Too large to display]

HoG graph id

45683

Graph name

n/a

Graph submitted by

Kolja Knauer

Invariant values

The definitions of the invariants can be found here.
Invariant Value Invariant Value
Acyclic No Index 6
Algebraic Connectivity 1.836 Laplacian Largest Eigenvalue 9.391
Average Degree 6 Longest Induced Cycle Computation time out
Bipartite No Longest Induced Path Computation time out
Chromatic Index Computation time out Matching Number 31
Chromatic Number 4 Maximum Degree 6
Circumference Computation time out Minimum Degree 6
Claw-Free No Minimum Dominating Set 12
Clique Number 3 Number of Components 1
Connected Yes Number of Edges 189
Density 0.097 Number of Triangles 42
Diameter 4 Number of Vertices 63
Edge Connectivity Computation time out Planar Computation time out
Eulerian Yes Radius 4
Genus Computation time out Regular Yes
Girth 3 Second Largest Eigenvalue 4.164
Hamiltonian Computation time out Smallest Eigenvalue -3.391
Independence Number 19 Vertex Connectivity Computation time out

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

Comments

Posted by Kolja Knauer at Sep 5, 2021 2:31 PM.
The minimal Cayley graph mininimizing alpha/n for n up to 95. It is a Cayley graph of Z_3 x (Z_7 ⋊ Z_3), with respect to two generators of order 3 and one of order 7.

Posted by Kolja Knauer at Sep 5, 2021 2:56 PM.
It is also a one of the small prime minimal Cayley graphs of chromatic number 4

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