Graph details

Graph # 33736

Adjacency matrix

[Too large to display]

Adjacency list

[Too large to display]

HoG graph id


Graph name

21,3 Symmetric Configuration Incidence Graph

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 0.706 Laplacian Largest Eigenvalue 6
Average Degree 3 Longest Induced Cycle 30
Bipartite Yes Longest Induced Path 28
Chromatic Index 3 Matching Number 21
Chromatic Number 2 Maximum Degree 3
Circumference 42 Minimum Degree 3
Claw-Free No Minimum Dominating Set 12
Clique Number 2 Number of Components 1
Connected Yes Number of Edges 63
Density 0.073 Number of Triangles 0
Diameter 6 Number of Vertices 42
Edge Connectivity 3 Planar No
Eulerian No Radius 5
Genus 5 Regular Yes
Girth 8 Second Largest Eigenvalue 2.294
Hamiltonian Yes Smallest Eigenvalue -3
Independence Number 21 Vertex Connectivity 3

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


Posted by Kevin Ryde at Jul 3, 2019 10:40 AM.
Betten, Brinkmann and Pisanskic give this as an example 21,3 symmetric configuration incidence graph (their figure 2). It is triangle-free, point transitive, block intransitive, and they construct by subdivision and addition to the Heawood graph (which is the sole 7,3 incidence graph).

Anton Betten, Gunnar Brinkmann, Tomaž Pisanskic, "Counting Symmetric Configurations v₃", Discrete Applied Mathematics, volume 99, 2000, pages 331–338.

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