Graph details

Graph # 33638

Adjacency matrix

[Too large to display]

Adjacency list

[Too large to display]

HoG graph id


Graph name

Transpose Covers 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 7.714
Algebraic Connectivity 0.852 Laplacian Largest Eigenvalue 15.806
Average Degree 7.4 Longest Induced Cycle Computation time out
Bipartite Yes Longest Induced Path Computation time out
Chromatic Index Computation time out Matching Number 60
Chromatic Number Computation time out Maximum Degree 9
Circumference Computation time out Minimum Degree 4
Claw-Free No Minimum Dominating Set Computation time out
Clique Number 2 Number of Components 1
Connected Yes Number of Edges 444
Density 0.062 Number of Triangles 0
Diameter 10 Number of Vertices 120
Edge Connectivity Computation time out Planar Computation time out
Eulerian No Radius 5
Genus Computation time out Regular No
Girth 4 Second Largest Eigenvalue 6.028
Hamiltonian Computation time out Smallest Eigenvalue -7.714
Independence Number Computation time out Vertex Connectivity Computation time out

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


Posted by Kevin Ryde at Mar 17, 2019 1:09 AM.
Each vertex is a permutation of integers 1..5, so 5!=120 vertices. Each edge is by swapping 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 444 is OEIS A002538.

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