Graph details

Graph # 500

Adjacency matrix

0001
0001
0001
1110

Adjacency list

1: 4
2: 4
3: 4
4: 1 2 3

HoG graph id

500

Graph name

Claw Graph

Graph submitted by

GraPHedron

Invariant values

The definitions of the invariants can be found here.
Invariant Value Invariant Value
Acyclic Yes Index 1.732
Algebraic Connectivity 1 Laplacian Largest Eigenvalue 4
Average Degree 1.5 Longest Induced Cycle undefined
Bipartite Yes Longest Induced Path 2
Chromatic Index 3 Matching Number 1
Chromatic Number 2 Maximum Degree 3
Circumference undefined Minimum Degree 1
Claw-Free No Minimum Dominating Set 1
Clique Number 2 Number of Components 1
Connected Yes Number of Edges 3
Density 0.5 Number of Triangles 0
Diameter 2 Number of Vertices 4
Edge Connectivity 1 Planar Yes
Eulerian No Radius 1
Genus 0 Regular No
Girth undefined Second Largest Eigenvalue 0
Hamiltonian No Smallest Eigenvalue -1.732
Independence Number 3 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 House of Graphs at Nov 26, 2015 11:31 AM.
One of the minimal forbidden induced subgraphs for graph class skript G: For all graphs G in skript G, \Delta(G) \leq \chi(G) + 1 holds for all induced subgraphs of G. See "O. Schaudt, V. Weil, On bounding the difference between the maximum degree and the chromatic number by a constant", submitted to Discrete Applied Mathematics, 2015.

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