Graph details

Graph # 334

Adjacency matrix

000010
000001
000001
000010
100101
011010

Adjacency list

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

HoG graph id

334

Graph name

H Graph

Graph submitted by

GraPHedron

Invariant values

The definitions of the invariants can be found here.
Invariant Value Invariant Value
Acyclic Yes Index 2
Algebraic Connectivity 0.438 Laplacian Largest Eigenvalue 4.562
Average Degree 1.667 Longest Induced Cycle undefined
Bipartite Yes Longest Induced Path 3
Chromatic Index 3 Matching Number 2
Chromatic Number 2 Maximum Degree 3
Circumference undefined Minimum Degree 1
Claw-Free No Minimum Dominating Set 2
Clique Number 2 Number of Components 1
Connected Yes Number of Edges 5
Density 0.333 Number of Triangles 0
Diameter 3 Number of Vertices 6
Edge Connectivity 1 Planar Yes
Eulerian No Radius 2
Genus 0 Regular No
Girth undefined Second Largest Eigenvalue 1
Hamiltonian No Smallest Eigenvalue -2
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.

Posted by MathWorld at Mar 28, 2012 11:57 AM.
Source: MathWorld and GraphData in Mathematica.

Posted by Danny Rorabaugh at Jun 16, 2016 8:48 PM.
"The Killer"
http://independencenumber.wordpress.com/2012/09/02/the-killer-appears/

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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