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 61000272 Title A name given to the resource A Study on Graph Colouring with Distance Constraints Subject The topic of the resource Mathematics and Statistics Description An account of the resource In this dissertation, we have studied the variations of graph colouring based on distance constraints. For a given set T of non-negative integers including zero and a positive integer k, the L(T,1)-colouring of a graph G = (V,E) is a function c : V(G) and#8594; newline{0,1,2,...,k} such that |c(u)and#8722;c(v)| and#8712;/ T if the distance between u and v is 1 and |c(u)and#8722; newlinec(v)| and#8805; 1 whenever u and v are at distance 2. The L(T,1)-span, and#955;T,1(G) is the smallest positive integer k such that G admits an L(T,1)-Colouring. We have determined the newlineL(T,1)-span for some classes of graphs for set T whose elements are arranged in arithmetic progression. Further, for any general set T , we have found the bound for L(T,1)- span of a few classes of graphs. We use Python programming to colour certain classes of graphs concerning L(T,1)-colouring and fnd the value of L(T,1)-span. Next, we have explored equitable fractional open neighbourhood colouring, which is an extension of a specifc variation of L(h,k)-Colouring for h = 0 and k = 1. For a newlinepositive integer p, equitable fractional open neighbourhood colouring of a graph G is an newlineassignment of positive integers to the vertices of G such that for each vertex v and#8712;V(G), vertices of N(v) receives at least l1p|N(v)|m distinct colours and N(v) can be partitioned into k-classes V1,V2,...Vk such that ||Vi|and#8722; |Vj|| and#8804; 1 for every i and#824;= j and 1 and#8804; k and#8804; n. The minimum number of colours required to colour G such that it admits equitable fractional open neighbourhood colouring for a fxed p is called the equitable fractional open neighbourhood chromatic number, and#967;eq onc newlinep (G). We have studied some properties of equitable fractional open neighbourhood colouring and explored some classes of graphs which admit equitable fractional open neighbourhood colouring with land#8710;(pG)m colours. Further, we have introduced and examined a variation of perfect graphs, and#967;onc-perfect graphs, with respect to equitable fractional open neighbourhood colouring for the special case of p = 1. Creator An entity primarily responsible for making the resource Pandey, Priyanka 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/10603/533986" target="_blank" rel="noreferrer noopener">http://hdl.handle.net/10603/533986</a>