Graph details

Graph # 34257

Adjacency matrix

[Too large to display]

Adjacency list

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HoG graph id


Graph name

Most Maximum Matchings Tree 27

Graph submitted by

Kevin Ryde

Invariant values

The definitions of the invariants can be found here.
Invariant Value Invariant Value
Acyclic Yes Index 2.449
Algebraic Connectivity 0.051 Laplacian Largest Eigenvalue 5.543
Average Degree 1.926 Longest Induced Cycle undefined
Bipartite Yes Longest Induced Path 8
Chromatic Index 4 Matching Number 8
Chromatic Number 2 Maximum Degree 4
Circumference undefined Minimum Degree 1
Claw-Free No Minimum Dominating Set 7
Clique Number 2 Number of Components 1
Connected Yes Number of Edges 26
Density 0.074 Number of Triangles 0
Diameter 8 Number of Vertices 27
Edge Connectivity 1 Planar Yes
Eulerian No Radius 4
Genus 0 Regular No
Girth undefined Second Largest Eigenvalue 2.175
Hamiltonian No Smallest Eigenvalue -2.449
Independence Number 19 Vertex Connectivity 1

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


Posted by Kevin Ryde at Feb 5, 2020 7:25 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=27. It has 5832 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.

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