Graph details

Graph # 34261

Adjacency matrix

[Too large to display]

Adjacency list

[Too large to display]

HoG graph id

34261

Graph name

Most Maximum Matchings Tree 29

Graph submitted by

Kevin Ryde

Invariant values

The definitions of the invariants can be found here.
Invariant Value Invariant Value
Acyclic Yes Index 2.441
Algebraic Connectivity 0.034 Laplacian Largest Eigenvalue 5.549
Average Degree 1.931 Longest Induced Cycle undefined
Bipartite Yes Longest Induced Path 12
Chromatic Index 4 Matching Number 8
Chromatic Number 2 Maximum Degree 4
Circumference undefined Minimum Degree 1
Claw-Free No Minimum Dominating Set 8
Clique Number 2 Number of Components 1
Connected Yes Number of Edges 28
Density 0.069 Number of Triangles 0
Diameter 12 Number of Vertices 29
Edge Connectivity 1 Planar Yes
Eulerian No Radius 6
Genus 0 Regular No
Girth undefined Second Largest Eigenvalue 2.257
Hamiltonian No Smallest Eigenvalue -2.441
Independence Number 21 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 7:28 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=29. It has 11455 maximum matchings (of size matchnum 8).

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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