What is the maximal connected partial symmetry index of a connected graph of a given size?
Z. Janelidze, F. van Niekerk, J. Viljoen
TL;DR
This paper determines the maximum connected partial symmetry index for connected graphs of a given size, quantifying the extent of symmetry among their connected induced subgraphs.
Contribution
It provides a definitive answer to the maximum possible connected partial symmetry index for connected graphs of any given order.
Findings
Identifies the maximum connected partial symmetry index for connected graphs.
Characterizes the graphs achieving this maximum.
Provides a formula or method to compute the index for given graph sizes.
Abstract
For a given graph, by its \emph{connected partial symmetry index} we mean the number of all isomorphisms between connected induced subgraphs of the graph. In this brief note we answer the question in the title.
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Taxonomy
TopicsGraph theory and applications · Graphene research and applications · Complex Network Analysis Techniques