Graph details

Graph # 30

Adjacency matrix

00001
00001
00010
00101
11010

Adjacency list

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

HoG graph id

30

Graph name

Fork Graph

Graph submitted by

GraPHedron

Invariant values

The definitions of the invariants can be found here.
Invariant Value Invariant Value
Acyclic Yes Index 1.848
Algebraic Connectivity 0.519 Laplacian Largest Eigenvalue 4.17
Average Degree 1.6 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 4
Density 0.4 Number of Triangles 0
Diameter 3 Number of Vertices 5
Edge Connectivity 1 Planar Yes
Eulerian No Radius 2
Genus 0 Regular No
Girth undefined Second Largest Eigenvalue 0.765
Hamiltonian No Smallest Eigenvalue -1.848
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.

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