Graph details

Graph # 32276

Adjacency matrix

[Too large to display]

Adjacency list

[Too large to display]

HoG graph id

32276

Graph name

Lex-Max Vpar Forests Differences N=5

Graph submitted by

Kevin Ryde

Invariant values

The definitions of the invariants can be found here.
Invariant Value Invariant Value
Acyclic No Index 4.546
Algebraic Connectivity 0.461 Laplacian Largest Eigenvalue 8.556
Average Degree 3.6 Longest Induced Cycle 6
Bipartite No Longest Induced Path 10
Chromatic Index 7 Matching Number 10
Chromatic Number 4 Maximum Degree 7
Circumference 15 Minimum Degree 1
Claw-Free No Minimum Dominating Set 5
Clique Number 4 Number of Components 1
Connected Yes Number of Edges 36
Density 0.189 Number of Triangles 14
Diameter 4 Number of Vertices 20
Edge Connectivity 1 Planar No
Eulerian No Radius 3
Genus 1 Regular No
Girth 3 Second Largest Eigenvalue 3.072
Hamiltonian No Smallest Eigenvalue -2.837
Independence Number 9 Vertex Connectivity 1

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

Comments

Posted by Kevin Ryde at Dec 16, 2018 2:45 AM.
Each graph vertex is an unlabelled rooted forest of n=5 vertices (20 of them) represented by a labelled rooted forest in vertex parent array form (vpar). Labelling is chosen to give each the lexicographically greatest vpar array. Graph edges are between arrays differing in one position.

The 2 degree-1 vertices are vpar=[0,0,0,0,0] singletons and vpar=[5,5,4,2,0] path-5. The latter has the degree-6 neighbour.

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