# Graph details

### Adjacency matrix

 0001 0001 0001 1110

### Adjacency list

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

500

Claw Graph

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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