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 61000259 Title A name given to the resource On the Maximization of Some Graph Coloring Problems Subject The topic of the resource Mathematics and Statistics Description An account of the resource A graph coloring problem involves labeling the vertices or edges in a graph with newlinecolors or numbers subject to some constraints. The most frequently known graph newlinecoloring problems are the ones that usually minimize the number of colors used in newlinecoloring the vertices or edges. The chromatic number of a graph G, denoted by and#967;(G), is the least number of colors used in a proper coloring of G. The chromatic sum of a graph G, denoted as P(G), was introduced in [1], which is to and the smallest possible coloring sum in a proper coloring of the graph G using natural numbers. Lately, a few studies have endured in a distinct area of the literature where the number of colors used in a graph coloring problem is maximized under certain conditions. Some of these works have applications in network sciences. newlineThe concerned study focuses on the maximization of three dierent edge coloring newlineconcepts, viz., the vertex induced kand#8722;edge coloring, vertex incident kand#8722;edge coloring, newlineand edge incident 2and#8722;edge coloring of a simple connected graph G, where k and#8805; 2. The newlinenumber of colors assigned to the edges of the graph G has been maximized under certain conditions. The vertex induced kand#8722;edge coloring and the vertex incident newlinekand#8722;edge coloring concepts are the generalized version of the edge coloring approach newlineintroduced and studied in [2]. Furthermore, the concept of the achromatic sum of a graph G has also been introduced here. This concept is to and the greatest possible coloring sum of the graph G in an improper edge coloring using natural numbers. An extensive study newlineon three achromatic sums, namely the vertex induced 2and#8722;edge coloring sum, the vertex incident 2and#8722;edge coloring sum, and the edge incident 2and#8722;edge coloring sum are carried out. A few bounds for these parameters on a simple connected graph G and the exact values for some elementary graph classes have been investigated. A few comparative results between some of these parameters have also been obtained. Creator An entity primarily responsible for making the resource Joseph, Anu 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 2023-01-01 Contributor An entity responsible for making contributions to the resource Dominic, Charles. 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/10603/527007" target="_blank" rel="noreferrer noopener">http://hdl.handle.net/10603/527007</a>