Graph details

Graph # 34265

Adjacency matrix

[Too large to display]

Adjacency list

[Too large to display]

HoG graph id

34265

Graph name

Most Maximum Matchings Tree 31

Graph submitted by

Kevin Ryde

Invariant values

The definitions of the invariants can be found here.
Invariant Value Invariant Value
Acyclic Yes Index 2.463
Algebraic Connectivity 0.038 Laplacian Largest Eigenvalue 5.571
Average Degree 1.935 Longest Induced Cycle undefined
Bipartite Yes Longest Induced Path 10
Chromatic Index 4 Matching Number 9
Chromatic Number 2 Maximum Degree 4
Circumference undefined Minimum Degree 1
Claw-Free No Minimum Dominating Set 9
Clique Number 2 Number of Components 1
Connected Yes Number of Edges 30
Density 0.065 Number of Triangles 0
Diameter 10 Number of Vertices 31
Edge Connectivity 1 Planar Yes
Eulerian No Radius 5
Genus 0 Regular No
Girth undefined Second Largest Eigenvalue 2.236
Hamiltonian No Smallest Eigenvalue -2.463
Independence Number 22 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 Feb 5, 2020 7:30 AM.
Heuberger and Wagner determine trees of n vertices with the most maximum matchings and show there is a unique such tree (except two each at n=6 and n=34). The present tree is n=31. It has 22140 maximum matchings (of size matchnum 9).

Clemens Heuberger and Stephan Wagner, "The Number of Maximum Matchings In a Tree", Discrete Mathematics, volume 311, issue 21, November 2011, pages 2512-2542. http://arxiv.org/abs/1011.6554

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