A survey on automorphism groups and transmission-based graph invariants

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Sharafdini Reza; Azadimotlagh Mehdi

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Journal Paper

Paper Information

Journal: Journal of Discrete Mathematics and its Applications Year:2024 | Volume:9 | Issue:2 Page(s): 133-145

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Title

A survey on automorphism groups and transmission-based graph invariants

Author(s)

Sharafdini Reza | Azadimotlagh Mehdi | Issue Writer Certificate

Keywords

Wiener index

hypercube graph

intersection graph

Kneser graph

Paley graph

Abstract

The distance $d(u,v)$ between vertices $u$ and $v$ of a connected graph $G$ is equal to the number of edges in a minimal path connecting them. The transmission of a vertex $v$ is defined by $\sigma(v)=\sum\limits_{u\in V(G)}{d(v,u)}$. A topological index is said to be a transmission-based topological index (TT index) if it includes the transmissions $\sigma(u)$ of vertices of $G$. Because $\sigma(u)$ can be derived from the distance matrix of $G$, it follows that transmission-based topological indices form a subset of distance-based topological indices.In this article we survey some results on the computation of some transmission-based graph invariants of intersection graph, hypercube graph, Kneser graph, unitary Cayley graph and Paley graph.

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