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 61000229 Title A name given to the resource A Study on Upper Domatic Number and Its Variants in Graphs Subject The topic of the resource Mathematics and Statistics Description An account of the resource For a graph G = (V, E), a vertex partition and#8673; = {V1, V2, . . . , Vk} is an upper domatic partition if Vi dominates Vj or Vj dominates Vi or both, for every Vi, Vj 2 and#8673;, whenever i 6= j. The upper domatic number D(G) is the maximum order of an upper domatic partition of G. This thesis consists of studies on upper domatic number and its variants in graphs. The bounds of D(G) in terms of order, size, !(G) and #(G) are established. The class of graphs with equal upper domatic newlinenumber and clique number is characterised. The relation between upper domatic number and minimum degree of the graph is explored. The case when the upper domatic number and domatic number are equal is investigated and the graphs for which D(G) and the domatic number d(G) coincide are characterised. Apart from the relation between the D(G) and other graph parameters, the upper domatic number of some special classes of graphs including unicyclic graphs, complement of cycles and powers of graphs is determined. Transitivity, Tr(G), a variant of upper domatic number is defined as the maximum number of sets in a vertex partition {V1, V2, . . . , Vk} such that Vi dominates Vj where 1 i lt j k. The results from the study on this concept include characterisation of graphs with transitivity at least k, exact values of transitivity of few classes of graphs, few upper bounds of transitivity of graphs, the transitivity of trees and an algorithm to determine the same. Along with this, the concept of total upper domatic number is introduced as a new variant of upper domatic number. The total upper domatic number is the maximum order of a total upper domatic partition of G which is an upper domatic partition such that the graph induced by each partite set does not contain any vertex of degree zero. Basic properties and bounds of upper domatic number in terms of order and maximum degree are discussed. Further, the total upper domatic number of some special classes of graphs is determined. Creator An entity primarily responsible for making the resource Samuel, Libin Chacko 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 Joseph, Mayamma. 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/10603/492348" target="_blank" rel="noreferrer noopener">http://hdl.handle.net/10603/492348</a>