A Study on Coloring Parameters and Topological Indices of Graphs

Title

A Study on Coloring Parameters and Topological Indices of Graphs

Creator

Glory,C

Contributor

Manjunath, N

Description

Graph coloring/labeling is a fundamental concept in graph theory that involves the assignment of weights, integers, or colors to the vertices/edges or both of a graph while adhering to specifc constraints. Graph colorings serve as a powerful mathematical model with broad applications in real-world scenarios, including network analysis, genomics, routing, optimization techniques, and digital networks. A research domain is established in which vertices of a graph are colored based on specifc conditions, and color degrees are taken into consideration leading to the exploration of chromatic topological indices and various chromatic polynomials. The introduction of chromatic topological indices in response to challenges in chemical graph theory has sparked signifcant research interest, creating a dynamic and expansive feld within graph theory. Motivated by this our study presents a comprehensive exploration of topological indices in the context of graph theory, specifcally focusing on the Zagreb index and its chromatic variants. The study calculates the frst and second rainbow chromatic Zagreb indices, rainbow chromatic irregularity indices, and rainbow chromatic total irregularity indices for well-known graph classes. Later, introduced the concept of b-chromatic Zagreb indices and b-chromatic irregularity indices and calculated the exact values for some standard graphs. Further, the rainbow chromatic topological indices and b-chromatic topological indices for various newlinederived graphs such as line, middle, total, and central graphs of some graph classes are determined. Novel graph polynomials, namely the b-chromatic Zagreb polynomials and b-chromatic irregularity polynomials, are introduced for some classes of graphs and the derived graphs such as degree splitting graph, mycielski graph. This comprehensive approach not only enhances our theoretical understanding of graph coloring but also oand#64256;ers practical insights into the predictive power of chromatic topological indices in diverse chemical contexts.

Source

Author's Submission

Date

2024-01-01

Publisher

Christ(Deemed to be University)

Subject

Mathematics and Statistics

Rights

Open Access

Relation

61000337

Format

PDF

Language

English

Type

PhD

Identifier

http://hdl.handle.net/10603/574690