Graph details

Graph # 260

Adjacency matrix

00000001
00000010
00011000
00100100
00100010
00010001
01001000
10000100

Adjacency list

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

HoG graph id

260

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 1.879
Algebraic Connectivity 0.152 Laplacian Largest Eigenvalue 3.848
Average Degree 1.75 Longest Induced Cycle undefined
Bipartite Yes Longest Induced Path 7
Chromatic Index 2 Matching Number 4
Chromatic Number 2 Maximum Degree 2
Circumference undefined Minimum Degree 1
Claw-Free Yes Minimum Dominating Set 3
Clique Number 2 Number of Components 1
Connected Yes Number of Edges 7
Density 0.25 Number of Triangles 0
Diameter 7 Number of Vertices 8
Edge Connectivity 1 Planar Yes
Eulerian No Radius 4
Genus 0 Regular No
Girth undefined Second Largest Eigenvalue 1.532
Hamiltonian No Smallest Eigenvalue -1.879
Independence Number 4 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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