Mathematics
https://hdl.handle.net/20.500.12818/22
Thu, 25 Apr 2024 05:38:28 GMT2024-04-25T05:38:28ZTransit in graphs
https://hdl.handle.net/20.500.12818/1514
Transit in graphs
Reshmi K M
In the thesis titled ’Transit in Graphs’, a graph invariant called ”Transit Index” is introduced. Analysis of the transit index in alkanes showed that the correlation between MON, a physical property of alkanes and this index is significant. The transit of a vertex in a graph is the sum of the length of all the shortest paths passing through it. The sum of the transit of every vertex in the graph is termed as transit index of a graph.Some bounds for the transit of a vertex are attained. Given the adjacency matrix of a graph, an effective method of computing the transit index is devised. The relationship between the transit index of a tree and its wiener index is
established. An expression for the transit index of a path is derived. It is established that the path has the maximum transit index among trees of the same order. Also, the transit index is computed for various graph classes.An investigation on how individual graph knowledge helps in the computation of transit of vertices/ transit index, in graph products is carried out. Transit equivalent class, transit dominant class and transit null graph are defined. The concept of majorized shortest paths, which facilitate the computation of the transit index of a graph is defined. Transit decomposition, which utilizes the notion of majorized shortest paths in a graph is studied. Transit decomposition number is defined and they are computed for a few graphs. Transit index and transit decomposition are explored in subdivision graphs.Graph isomorphism is a phenomenon in which the same graph appears in
different forms. In Chapter 6 we look at graphs displaying similar transit decom position. Such graphs are termed transit isomorphic. The occurrence of transit isomorphism between a graph and its line graph is investigated. We also identify certain graph classes that are transit isomorphic to each other.Amalgamations can reduce a graph to a simpler graph while keeping certain structures intact. Transit of vertices in the convex amalgamation of graphs is studied. The transit index being graph invariant finds application in chemical graph theory. The transit of a vertex can be treated as a centrality measure in networks. It was established that the transit index of alkanes has a strong correlation with the physical property MON (motor octane number). Transit decomposition also gives an insight into this physical property. In transportation networks, the concept of the transit of a vertex can be a functional tool.
Thesis (Ph.D)- Department of Mathematics, University of Calicut, 2023
Sun, 01 Jan 2023 00:00:00 GMThttps://hdl.handle.net/20.500.12818/15142023-01-01T00:00:00ZA study on cayley fuzzy graphs and cayley fuzzy graph structures
https://hdl.handle.net/20.500.12818/1497
A study on cayley fuzzy graphs and cayley fuzzy graph structures
Neethu K T
As most of real life problems deals with vague or imprecise concepts, the theory of fuzzy sets has a wider application than that of classical theories. The fuzzy set is a generalisation of fundamental mathematical concept of a set. Most of the mathematical theories can be extended using the concepts of a fuzzy set and fuzzy logic. A few among the real world problems where this theory has application are pattern recognition, information processing, increasing the efficiency of a system and multivalued decision processing. Similarly the theory of graphs is an extremely useful tool for solving combinatorial problems in different areas such as geometry, algebra, number theory, topology, operation research, optimization, and computer science. This thesis mainly deals with the study of Cayley fuzzy graphs and digraph structures induced by some algebraic structures. Many graph properties are expressed in terms of algebraic properties. Main focus is on the study of Cayley fuzzy graphs, Cayley bipolar fuzzy graphs and Cayley intuitionistic fuzzy graphs induced by loops, a weaker structure than groups. Moreover, we study Cayley fuzzy digraph structure and Cayley bipolar fuzzy digraph structure induced by groups and loops. The concepts of Cayley fuzzy graphs were first introduced and studied by Namboothiri et. al.. A nat- ural question is: Does weaker algebraic structure induce Cayley fuzzy graphs? Here in this thesis we prove that the algebraic structure loop induces Cayley fuzzy/bipolar fuzzy graphs and structures.This thesis comprises of six chapters. The first chapter contains the preliminary definitions and results that were used in the remaining chapters. In second chapter, we introduced the concept of Cayley fuzzy graphs induced by loops and studied graph theoretic properties in terms of algebraic properties. In the third chapter we introduced Cayley bipolar fuzzy graphs induced by loops and studied many basic properties. In fourth chapter Cayley intuitionistic fuzzy graph is defined. In the next two chapters, fifth and sixth, we extend our studies to digraph structures induced by groups and also to those induced by loops.
Thesis (Ph.D)- University of Calicut, Department of Mathematics, 2022
Sat, 01 Jan 2022 00:00:00 GMThttps://hdl.handle.net/20.500.12818/14972022-01-01T00:00:00ZA study on strength of strong fuzzy graphs and extra strong k- path domination in strong fuzzy graphs
https://hdl.handle.net/20.500.12818/752
A study on strength of strong fuzzy graphs and extra strong k- path domination in strong fuzzy graphs
Chitra K P
Mon, 01 Jan 2018 00:00:00 GMThttps://hdl.handle.net/20.500.12818/7522018-01-01T00:00:00ZOn the study of some problems in spectral sets, duggal transformations, and aluthge transformations
https://hdl.handle.net/20.500.12818/364
On the study of some problems in spectral sets, duggal transformations, and aluthge transformations
Saji Mathew
Thesis (Ph. D.)--University of Calicut, Department of Mathematics, 2008.
Tue, 01 Jan 2008 00:00:00 GMThttps://hdl.handle.net/20.500.12818/3642008-01-01T00:00:00Z