A study on graph decompositions

Abstract

This thesis embodies the work done by the author under the guidance of Dr. R. newlineKala, Associate Professor, Department of Mathematics, Manonmaniam Sundaranar newlineUniversity, Tirunelveli. newlineThe origin of the study of graph decompositions can be seen in various combi- newlinenatorial problems , most of which emerged in the 19th century. Among them the newlinebest known are Kirkman s problem of 15 strolling schoolgirls, Dudeney s problem of newline9 handcuffed prisoners, Euler s problem of 36 army officers, Kirkman s problem of newlineknights, Lucas dancing rounds problem and the four colour problem. However, the newlineearliest works in this direction are not explicitly related to graph decompositions. newlineSince that time the interest in graph decompositions has been on increase and a real newlineupsurge is witnessed after 1950. Nowadays, graph decompositions rank among the newlinemost prominent areas of graph theory and combinatorics. newlineMany combinatorial, algebraic and other mathematical structures are linked to newlinedecompositions of graph, which gives their study a great theoretical importance. newlineOn the other hand, results on graph decompositions can be applied in coding the- newlineory, design of experiments, X-ray crystallography, radioastronomy, radiolocation, newlinecomputer and communication networks, serology and other fields. newline