Graph details

Graph # 19655

Adjacency matrix

01
10

Adjacency list

1: 2
2: 1

HoG graph id

19655

Graph name

K_2, Complete Graph on 2 Vertices

Graph submitted by

Danny Rorabaugh

Invariant values

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

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

Comments

Posted by Danny Rorabaugh at Feb 26, 2015 7:25 PM.
Hartsfield and Ringel conjecture that K_2 is the only connected graph that is not antimagic. N. Hartsfield and G. Ringel, Pearls in Graph Theory, Academic Press, San Diego, 1990.

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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