Graph details

Graph # 684

Adjacency matrix

01000000
10000000
00010000
00100000
00000100
00001000
00000001
00000010

Adjacency list

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

HoG graph id

684

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
Algebraic Connectivity 0 Laplacian Largest Eigenvalue 2
Average Degree 1 Longest Induced Cycle undefined
Bipartite Yes Longest Induced Path 1
Chromatic Index 1 Matching Number 4
Chromatic Number 2 Maximum Degree 1
Circumference undefined Minimum Degree 1
Claw-Free Yes Minimum Dominating Set 4
Clique Number 2 Number of Components 4
Connected No Number of Edges 4
Density 0.143 Number of Triangles 0
Diameter infinity Number of Vertices 8
Edge Connectivity 0 Planar Yes
Eulerian No Radius undefined
Genus undefined Regular Yes
Girth undefined Second Largest Eigenvalue 1
Hamiltonian No Smallest Eigenvalue -1
Independence Number 4 Vertex Connectivity 0

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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