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 61000193 Title A name given to the resource A Study on defective colouring of graphs Subject The topic of the resource Mathematics and Statistics Description An account of the resource If different technology represents distinct colours that are to be located on some geographical region which can be represented as vertices of a graph, then the proper colouring is obtained when no two technology of same type share a common edge between the vertices they are placed on. The minimum number of technology required for such a colouring of a graph is the chromatic number of the graph. However, if the available technology are less than that of the minimum required, then the question arises on how to place the technology on the vertices of a graph in such a way that there is a minimum adjacency between the technology of same type. The solution for this problem can be attained by defining certain rules for the properness of colouring in which a few thresholds are tolerated. We know that, in a proper colouring every colour class is an independent set. If the available colours to colour a graph is less than that of the chromatic number of graphs, then a threshold that can be tolerated is permitting few colour classes to be non-independent set. An edge uv is said to be a monochromatic edge or bad edge if the colours assigned to both u and v are the same. A near proper colouring of graphs is a colouring that minimises the number of monochromatic edges by permitting few colour classes to have adjacency between the elements in it. The minimum number of monochromatic edges obtained from near proper colouring is called near defect number, denoted by B_k (G). A and#948;^((k))-colouring of graph G is a near proper colouring of G consisting of k given colours, where 1and#8804;kand#8804;and#967;(G)-1, which minimises the number of monochromatic edges by permitting at most one colour class to have adjacency among the vertices in it. The and#948;^((k))-defect number is the minimum number of monochromatic edges obtained from a and#948;^((k))-colouring of graphs and it is denoted by b_k(G). The study concerned is the further work on a near proper colouring and a and#948;^((k))-colouring of graphs. Creator An entity primarily responsible for making the resource Merlin Thomas, Ellumkalayil. 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 2022-01-01 Contributor An entity responsible for making contributions to the resource N K, Sudev 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/10603/401298" target="_blank" rel="noreferrer noopener">http://hdl.handle.net/10603/401298</a>