Harmonic Index of Total Graphs of Some Graphs

TL;DR

This paper investigates the harmonic index of total graphs derived from various standard graph types, including bipartite, regular, grid, and binary trees, providing insights into their spectral properties.

Contribution

It introduces the calculation of the harmonic index for total graphs of specific graph classes, expanding understanding of spectral graph invariants.

Findings

Harmonic index values for total bipartite graphs

Harmonic index for regular total graphs

Results for grid and binary tree total graphs

Abstract

Let G = G(V,E) be a graph with | V | vertices and | E | edges and total graph, T(G) is obtained from G. In This paper we have study the Harmonic index of total graph for standards graphs, bipartite graph of particular type, regular graph, Grid graph Gm,n and Complete Binary tree.