A Novel Approach to Topological Indices of the Identity Graph Associated with the Finite Group

Abstract

Graph theory is applied to study network structures in various disciplines, such as computer science and discrete mathematics. The combination of graphs and algebra has become a widely discussed topic in research within the fields of algebra and combinatorics. Research on group representations on graphs and topological indices has been extensively conducted, one such example is on the identity graph. A identity graph of a group $G$ which is an ordered pair $V(G)$ and $E(G)$, where all elements of $G$ serve as vertices, and two vertices $x,y \in G$ are adjacent if and only if $x*y=e$. This study proposes an alternative approach to calculating topological indices in the identity graph of the multiplicative group of integers modulo n.