Generalized Vertex Transitivity in Graphs
Kannan Balakrishnan, Divya Sindhu Lekha, Manoj Changat, Bijo S. Anand,, Prasanth G. Narasimha-Shenoi
TL;DR
This paper introduces a generalized concept of vertex transitivity in graphs, along with a new invariant called the transitivity number, and explores its values across various graph classes to demonstrate its significance.
Contribution
It proposes the transitivity number as a new invariant for graphs and investigates its properties across different graph classes.
Findings
Transitivity number varies across graph classes
New insights into graph symmetry properties
Potential applications in graph classification
Abstract
In this paper, we introduce a generalized concept of vertex transitivity in graphs called generalized vertex transitivity. We put forward a new invariant called transitivity number of a graph. The value of this invariant in different classes of graphs is explored. Also, different results showing the importance of this concept is established.
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Taxonomy
TopicsAdvanced Graph Theory Research · Finite Group Theory Research · Graph theory and applications