Triple Domination in Interval and Circular ARC Graphs

Abstract

Graph theory is a branch of mathematics that deals with the study of graphs. Graphs are mathematical structures used to represent pairwise relations between objects. A graph is com posed of vertices or nodes that are connected by edges or links. There are two types of graphs undirected and directed graphs: undirected graphs, where edges link two vertices symmetrically. and directed graphs, where edges link two vertices asymmetrically. Graphs are one of the primary objects of study in discrete mathematics. In the field of graph theory, a dominating set refers to a subset of vertices within a graph, where every vertex in the graph is either a member of the set or has at least one neighbor [73], in the set. Dominating sets have practical applications in various domains, such as wireless networking, where they help in finding efficient routes in ad-hoc mobile networks. They have also been used in document summarization and in the design of secure electrical grid systems. Leonard Euler, the renowned mathematician, proposed the fundamental concepts of graph theory in the 18th century. Since then, a great deal of study has grown interested in graph theory as a result of its significant progress that happened very quickly, inspired to a greater extent. This may have something to do with the increasing significance of computer science and graph theory. The study of graph theory is quite interesting. Graph theory is currently one of the most active areas in contemporary mathematics. Due to its numerous applications to discrete optimisation, combinatorial, and classical algebraic problems, graph theory has grown dramatically during the last 30 years. A straightforward method of illustrating a system s structure is through the use of graphs, which are just basic diagrams with points (vertices) and lines (edges). Graphs are helpful in improving our comprehension of computer systems behavioural traits and or ganisational structure. When addressing problems, its mathematical elegance and rigour are evident. Graph models are...