A Study of Directed Graph and Related Computer Programming

The present Ph. D. Thesis has been divided into seven chapters: I-VII, which deals with introduction, review of literature, isomorphism of directed graphs by considering graph invariant that is probability propagation matrix and related computer programming in C++ language; decyclization of directed graph and its isomorphic image by using combinatorial algorithm and related computer programming in C++ language; and pebbling on directed graphs. Chapter I presents the essential preliminaries related to graph, directed graph, review of literature, history, development, and the applications of graph theory in inter-disciplinary fields. Chapter II discusses graph isomorphism of undirected plane graphs. Chapter III presents a generalized heuristic program as a certificate for testing graph isomorphism by using C++ programming. Chapter IV is devoted to the study of decyclization in directed graphs and its isomorphic image by considering combinatorial approach. Chapter V discusses some aspects of combinatorial algorithms for feedback problems in directed graphs and presents a generalized heuristic program DTCPP. Chapter VI and VII discusses pebbling on undirected graphs and directed graphs.