Graph details

Graph # 1310

Adjacency matrix

0

Adjacency list

1:

HoG graph id

1310

Graph name

Singleton Graph

Graph submitted by

MathWorld

Invariant values

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

A table row rendered like this indicates that the graph is marked as being interesting for that invariant.

Comments

Posted by MathWorld at Mar 28, 2012 11:58 AM.
Source: MathWorld and GraphData in Mathematica.

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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