Graph details

Graph # 21063

Adjacency matrix

0111100000
1001001010
1000100101
1100100010
1011000001
0000001111
0100010110
0010011001
0101011000
0010110100

Adjacency list

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

HoG graph id

21063

Graph name

n/a

Graph submitted by

Jan Goedgebeur

Invariant values

The definitions of the invariants can be found here.
Invariant Value Invariant Value
Acyclic No Index 4
Algebraic Connectivity 1.764 Laplacian Largest Eigenvalue 6.236
Average Degree 4 Longest Induced Cycle 6
Bipartite No Longest Induced Path 5
Chromatic Index 4 Matching Number 5
Chromatic Number 4 Maximum Degree 4
Circumference 10 Minimum Degree 4
Claw-Free Yes Minimum Dominating Set 2
Clique Number 3 Number of Components 1
Connected Yes Number of Edges 20
Density 0.444 Number of Triangles 10
Diameter 3 Number of Vertices 10
Edge Connectivity 4 Planar Yes
Eulerian Yes Radius 3
Genus 0 Regular Yes
Girth 3 Second Largest Eigenvalue 2.236
Hamiltonian Yes Smallest Eigenvalue -2.236
Independence Number 3 Vertex Connectivity 4

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

Comments

Posted by Jan Goedgebeur at Jun 15, 2015 10:55 AM.
Vertex-transitive 4-vertex-critical P7-free graph.

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