Graph details

Graph # 49225

Adjacency matrix

[Too large to display]

Adjacency list

[Too large to display]

HoG graph id


Graph name


Graph submitted by

Gunnar Brinkmann

Invariant values

The definitions of the invariants can be found here.
Invariant Value Invariant Value
Acyclic No Index 4
Algebraic Connectivity 0.619 Laplacian Largest Eigenvalue 6.798
Average Degree 4 Longest Induced Cycle 14
Bipartite No Longest Induced Path 13
Chromatic Index 5 Matching Number 11
Chromatic Number 4 Maximum Degree 4
Circumference 22 Minimum Degree 4
Claw-Free No Minimum Dominating Set 5
Clique Number 3 Number of Components 1
Connected Yes Number of Edges 44
Density 0.19 Number of Triangles 15
Diameter 4 Number of Vertices 22
Edge Connectivity 4 Planar No
Eulerian Yes Radius 4
Genus 1 Regular Yes
Girth 3 Second Largest Eigenvalue 3.381
Hamiltonian Yes Smallest Eigenvalue -2.798
Independence Number 8 Vertex Connectivity 4

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


Posted by Gunnar Brinkmann at Jun 3, 2022 9:53 AM.
A smallest (uniqueness not yest tested -- 03/06/2022) 4-regular 4-vertex-connected graph of even order that is class 2 -- that is: has chromatic index 5

Posted by Gunnar Brinkmann at Jun 7, 2022 1:05 PM.
It is not unique. Graph 49231 has the same properties. This graph as well as 49231 can be obtained from 48188 by replacing a vertex in the 3-cut by a K_5 with two independent edges broken open.

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