Graph details

Graph # 33982

Adjacency matrix

011110000000
100010000011
100110000001
101010000001
111100000000
000000110011
000001011100
000001101100
000000110110
000000111010
010001001100
011101000000

Adjacency list

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

HoG graph id

33982

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
Algebraic Connectivity 0.438 Laplacian Largest Eigenvalue 7
Average Degree 4 Longest Induced Cycle 4
Bipartite No Longest Induced Path 5
Chromatic Index 4 Matching Number 6
Chromatic Number 4 Maximum Degree 4
Circumference 12 Minimum Degree 4
Claw-Free No Minimum Dominating Set 3
Clique Number 4 Number of Components 1
Connected Yes Number of Edges 24
Density 0.364 Number of Triangles 12
Diameter 4 Number of Vertices 12
Edge Connectivity 2 Planar No
Eulerian Yes Radius 3
Genus 2 Regular Yes
Girth 3 Second Largest Eigenvalue 3.562
Hamiltonian Yes Smallest Eigenvalue -3
Independence Number 4 Vertex Connectivity 2

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 26, 2019 12:34 PM.
A 4-regular nut graph. See "P.W. Fowler, J.B. Gauci, J. Goedgebeur, T. Pisanski and I. Sciriha, Existence of d-regular nut graphs for d at most 11, submitted" for more information.

You need to be logged in to be able to add comments.