Graph details

Graph # 32232

Adjacency matrix

000110100
000011001
000101010
101000101
110000011
011000110
100101011
001011101
010110110

Adjacency list

1: 4 5 7
2: 5 6 9
3: 4 6 8
4: 1 3 7 9
5: 1 2 8 9
6: 2 3 7 8
7: 1 4 6 8 9
8: 3 5 6 7 9
9: 2 4 5 7 8

HoG graph id

32232

Graph name

Deleted Edge Symmetric, from No Add Edge, N=9

Graph submitted by

Kevin Ryde

Invariant values

The definitions of the invariants can be found here.
Invariant Value Invariant Value
Acyclic No Index 4.162
Algebraic Connectivity 2.209 Laplacian Largest Eigenvalue 6.791
Average Degree 4 Longest Induced Cycle 6
Bipartite No Longest Induced Path 4
Chromatic Index 5 Matching Number 4
Chromatic Number 3 Maximum Degree 5
Circumference 9 Minimum Degree 3
Claw-Free No Minimum Dominating Set 3
Clique Number 3 Number of Components 1
Connected Yes Number of Edges 18
Density 0.5 Number of Triangles 7
Diameter 2 Number of Vertices 9
Edge Connectivity 3 Planar No
Eulerian No Radius 2
Genus 1 Regular No
Girth 3 Second Largest Eigenvalue 1.303
Hamiltonian Yes Smallest Eigenvalue -2.303
Independence Number 3 Vertex Connectivity 3

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

Comments

Posted by Kevin Ryde at Nov 5, 2018 2:04 AM.
There are two graphs of n=9 vertices which are asymmetric and can be made symmetric by deleting one edge, but cannot be made symmetric by adding one edge. The delete in each case results in the same symmetric, being the present graph. It has automorphism group C3.

One of the "can delete, cannot add" is reached by edge between two degree-4s. The other is reached by edge between a degree-3 and degree-5 to create a clique-4.

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