Graph details

Graph # 33636

Adjacency matrix

[Too large to display]

Adjacency list

[Too large to display]

HoG graph id

33636

Graph name

Transpose Covers N=4

Graph submitted by

Kevin Ryde

Invariant values

The definitions of the invariants can be found here.
Invariant Value Invariant Value
Acyclic No Index 5.008
Algebraic Connectivity 1.087 Laplacian Largest Eigenvalue 10.25
Average Degree 4.833 Longest Induced Cycle 12
Bipartite Yes Longest Induced Path 12
Chromatic Index 6 Matching Number 12
Chromatic Number 2 Maximum Degree 6
Circumference 24 Minimum Degree 3
Claw-Free No Minimum Dominating Set 4
Clique Number 2 Number of Components 1
Connected Yes Number of Edges 58
Density 0.21 Number of Triangles 0
Diameter 6 Number of Vertices 24
Edge Connectivity 3 Planar No
Eulerian No Radius 3
Genus 4 Regular No
Girth 4 Second Largest Eigenvalue 3.171
Hamiltonian Yes Smallest Eigenvalue -5.008
Independence Number 12 Vertex Connectivity 3

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

Comments

Posted by Kevin Ryde at Mar 17, 2019 1:08 AM.
Each vertex is a permutation of integers 1..4, so 4!=24 vertices. Each edge is by swapping two elements to reach a lexicographically bigger permutation, and where not already reached by some longer chain of transpositions (so Hasse diagram, equivalent to number of "inversions" increase by 1). Number of edges 58 is OEIS A002538.

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