Dublin Core The Dublin Core metadata element set is common to all Omeka records, including items, files, and collections. For more information see, http://dublincore.org/documents/dces/. Title A name given to the resource PHD PhD PhD Thesis Dublin Core The Dublin Core metadata element set is common to all Omeka records, including items, files, and collections. For more information see, http://dublincore.org/documents/dces/. Relation A related resource 61000337 Title A name given to the resource A Study on Coloring Parameters and Topological Indices of Graphs Subject The topic of the resource Mathematics and Statistics Description An account of the resource 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. Creator An entity primarily responsible for making the resource Glory,C Source A related resource from which the described resource is derived Author's Submission Publisher An entity responsible for making the resource available Christ(Deemed to be University) Date A point or period of time associated with an event in the lifecycle of the resource 2024-01-01 Contributor An entity responsible for making contributions to the resource Manjunath, N Rights Information about rights held in and over the resource Open Access Format The file format, physical medium, or dimensions of the resource PDF Language A language of the resource English Type The nature or genre of the resource PhD Identifier An unambiguous reference to the resource within a given context <a href="http://hdl.handle.net/10603/574690" target="_blank" rel="noreferrer noopener">http://hdl.handle.net/10603/574690</a>