Graph details

Graph # 28500

Adjacency matrix

[Too large to display]

Adjacency list

[Too large to display]

HoG graph id


Graph name

Hex Grid 3,3,3

Graph submitted by

Kevin Ryde

Invariant values

The definitions of the invariants can be found here.
Invariant Value Invariant Value
Acyclic No Index 2.84
Algebraic Connectivity 0.111 Laplacian Largest Eigenvalue 5.803
Average Degree 2.667 Longest Induced Cycle 36
Bipartite Yes Longest Induced Path 38
Chromatic Index 3 Matching Number 27
Chromatic Number 2 Maximum Degree 3
Circumference 52 Minimum Degree 2
Claw-Free No Minimum Dominating Set 15
Clique Number 2 Number of Components 1
Connected Yes Number of Edges 72
Density 0.05 Number of Triangles 0
Diameter 11 Number of Vertices 54
Edge Connectivity 2 Planar Yes
Eulerian No Radius 7
Genus 0 Regular No
Girth 6 Second Largest Eigenvalue 2.604
Hamiltonian No Smallest Eigenvalue -2.84
Independence Number 27 Vertex Connectivity 2

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


Posted by Kevin Ryde at Aug 13, 2017 4:48 AM.
This is the game grid of the Settlers of Catan board game. Players build cities on vertices and roads on edges. The 6-cycles enclose various forest etc which generate timber etc for cities on those vertices.

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