Graph details

Graph # 49229

Adjacency matrix

011111000000
100000101110
100110010001
101001000011
101001000101
100110001001
010000011011
001000101110
010001110100
010010011010
010100110100
001111100000

Adjacency list

1: 2 3 4 5 6
2: 1 7 9 10 11
3: 1 4 5 8 12
4: 1 3 6 11 12
5: 1 3 6 10 12
6: 1 4 5 9 12
7: 2 8 9 11 12
8: 3 7 9 10 11
9: 2 6 7 8 10
10: 2 5 8 9 11
11: 2 4 7 8 10
12: 3 4 5 6 7

HoG graph id

49229

Graph name

n/a

Graph submitted by

Steven Van Overberghe

Invariant values

The definitions of the invariants can be found here.
Invariant Value Invariant Value
Acyclic No Index 5
Algebraic Connectivity 2 Laplacian Largest Eigenvalue 7.732
Average Degree 5 Longest Induced Cycle 5
Bipartite No Longest Induced Path 5
Chromatic Index 5 Matching Number 6
Chromatic Number 3 Maximum Degree 5
Circumference 12 Minimum Degree 5
Claw-Free No Minimum Dominating Set 3
Clique Number 3 Number of Components 1
Connected Yes Number of Edges 30
Density 0.455 Number of Triangles 16
Diameter 2 Number of Vertices 12
Edge Connectivity 5 Planar No
Eulerian No Radius 2
Genus 1 Regular Yes
Girth 3 Second Largest Eigenvalue 3
Hamiltonian Yes Smallest Eigenvalue -2.732
Independence Number 4 Vertex Connectivity 5

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

Comments

Posted by Steven Van Overberghe at Jun 6, 2022 11:22 AM.
One of two smallest (order, then size) vertex-transitive graphs with the minimal amount of automorphisms (that is: equal to the order) [excluding trivial graphs of order less than 3].

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