Graph details

Graph # 44105

Adjacency matrix

[Too large to display]

Adjacency list

[Too large to display]

HoG graph id


Graph name

Hanoi Exchanging Discs, 3 Discs

Graph submitted by

Kevin Ryde

Invariant values

The definitions of the invariants can be found here.
Invariant Value Invariant Value
Acyclic No Index 3.132
Algebraic Connectivity 0.164 Laplacian Largest Eigenvalue 6.439
Average Degree 2.889 Longest Induced Cycle 6
Bipartite No Longest Induced Path 13
Chromatic Index 4 Matching Number 13
Chromatic Number 3 Maximum Degree 4
Circumference 27 Minimum Degree 2
Claw-Free No Minimum Dominating Set 9
Clique Number 3 Number of Components 1
Connected Yes Number of Edges 39
Density 0.111 Number of Triangles 9
Diameter 7 Number of Vertices 27
Edge Connectivity 2 Planar Yes
Eulerian No Radius 5
Genus 0 Regular No
Girth 3 Second Largest Eigenvalue 2.704
Hamiltonian Yes Smallest Eigenvalue -2.618
Independence Number 9 Vertex Connectivity 2

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


Posted by Kevin Ryde at Feb 23, 2021 8:40 AM.
Scorer, Grundy and Smith define a variation of the towers of Hanoi puzzle where the smallest disk moves freely and two disks can exchange positions when they differ in size by 1, are on different pegs, and each is top-most on its peg. Each vertex here is a configuration of discs on spindles. Each edge is a step (move or exchange) between configurations.

R. S. Scorer, P. M. Grundy and C. A. B. Smith, "Some Binary Games", The Mathematical Gazette, July 1944, volume 28, number 280, pages 96-103,, section 4(iii). The drawing here is per their figure 4.

Paul K. Stockmeyer et al, "Exchanging Disks in the Tower of Hanoi", International Journal of Computer Mathematics, volume 59, number 1-2, pages 37-47, 1995,, calculating the graph diameter (OEIS A341579).

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