Graph details

Graph # 60

Adjacency matrix

0000000100000
0000000010000
0000000001000
0000000000100
0000000000001
0000000000001
0000000000010
1000000010000
0100000101000
0010000010100
0001000001010
0000001000101
0000110000010

Adjacency list

1: 8
2: 9
3: 10
4: 11
5: 13
6: 13
7: 12
8: 1 9
9: 2 8 10
10: 3 9 11
11: 4 10 12
12: 7 11 13
13: 5 6 12

HoG graph id

60

Graph name

n/a

Graph submitted by

GraPHedron

Invariant values

The definitions of the invariants can be found here.
Invariant Value Invariant Value
Acyclic Yes Index 2.275
Algebraic Connectivity 0.109 Laplacian Largest Eigenvalue 5.038
Average Degree 1.846 Longest Induced Cycle undefined
Bipartite Yes Longest Induced Path 7
Chromatic Index 3 Matching Number 6
Chromatic Number 2 Maximum Degree 3
Circumference undefined Minimum Degree 1
Claw-Free No Minimum Dominating Set 6
Clique Number 2 Number of Components 1
Connected Yes Number of Edges 12
Density 0.154 Number of Triangles 0
Diameter 7 Number of Vertices 13
Edge Connectivity 1 Planar Yes
Eulerian No Radius 4
Genus 0 Regular No
Girth undefined Second Largest Eigenvalue 1.893
Hamiltonian No Smallest Eigenvalue -2.275
Independence Number 7 Vertex Connectivity 1

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

Comments

Posted by GraPHedron at Mar 28, 2012 11:56 AM.
Is an extremal graph found by GraPHedron. See "H. Melot, Facet defining inequalities among graph invariants: the system graphedron. Discrete Applied Mathematics 156 (2008), 1875-1891" for more information.

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