Graph details

Graph # 670

Adjacency matrix

011000
100010
100001
000011
010100
001100

Adjacency list

1: 2 3
2: 1 5
3: 1 6
4: 5 6
5: 2 4
6: 3 4

HoG graph id

670

Graph name

n/a

Graph submitted by

GraPHedron

Invariant values

The definitions of the invariants can be found here.
Invariant Value Invariant Value
Acyclic No Index 2
Algebraic Connectivity 1 Laplacian Largest Eigenvalue 4
Average Degree 2 Longest Induced Cycle 6
Bipartite Yes Longest Induced Path 4
Chromatic Index 2 Matching Number 3
Chromatic Number 2 Maximum Degree 2
Circumference 6 Minimum Degree 2
Claw-Free Yes Minimum Dominating Set 2
Clique Number 2 Number of Components 1
Connected Yes Number of Edges 6
Density 0.4 Number of Triangles 0
Diameter 3 Number of Vertices 6
Edge Connectivity 2 Planar Yes
Eulerian Yes Radius 3
Genus 0 Regular Yes
Girth 6 Second Largest Eigenvalue 1
Hamiltonian Yes Smallest Eigenvalue -2
Independence Number 3 Vertex Connectivity 2

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.

Posted by House of Graphs at Jan 29, 2019 9:24 AM.
A connected integral graph. A graph is called integral if all of its eigenvalues of its adjacency matrix are integral. See "Krzysztof T. ZwierzyƄski, Generating Integral Graphs Using PRACE Research Infrastructure" for more information.

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