Graph details

Graph # 45679

Adjacency matrix

010010101
100010101
000101011
001001011
110001100
001110010
110010011
001101101
111100110

Adjacency list

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

HoG graph id

45679

Graph name

n/a

Graph submitted by

House of Graphs

Invariant values

The definitions of the invariants can be found here.
Invariant Value Invariant Value
Acyclic No Index 4.545
Algebraic Connectivity 1.597 Laplacian Largest Eigenvalue 7.303
Average Degree 4.444 Longest Induced Cycle 5
Bipartite No Longest Induced Path 3
Chromatic Index 6 Matching Number 4
Chromatic Number 5 Maximum Degree 6
Circumference 9 Minimum Degree 4
Claw-Free Yes Minimum Dominating Set 2
Clique Number 4 Number of Components 1
Connected Yes Number of Edges 20
Density 0.556 Number of Triangles 15
Diameter 2 Number of Vertices 9
Edge Connectivity 4 Planar No
Eulerian No Radius 2
Genus 1 Regular No
Girth 3 Second Largest Eigenvalue 2.562
Hamiltonian Yes Smallest Eigenvalue -2
Independence Number 2 Vertex Connectivity 3

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

Comments

Posted by House of Graphs at Aug 10, 2021 11:45 AM.
A 5-vertex-critical (P5,(P2+P3)^c)-free graph. Keyword: 5-critical P5co(P2+P3)-free. See "Q. Cai, J. Goedgebeur and S. Huang, Some Results on k-Critical P5-Free Graphs, manuscript, 2021" for more details".

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