Studies on graph labeling problems

Abstract

The thesis entitled Studies on Graph Labeling Problems embodies the work newlinedone by A.Ponmoni, Assistant Professor of Mathematics, C.S.I College of newlineEngineering, Ketti, under the guidance of Dr.S.Navaneethakrishnan, Associate newlineProfessor, S.S.Pillai Centre for Research in Mathematics, V.O.Chidambaram newlineCollege, Thoothukudi. newlineThis thesis comprises of the following five chapters. newline1. Preliminaries newline2. Total Edge Lucas Irregular Labeling newline3. Lucas Mean Graphs newline4. Skolem Difference Lucas Mean Graphs newline5. Triangular Divisor Cordial graphs newlineBy a graph G (V, E) it means a finite, undirected graph with neither loops nor newlinemultiple edges. For graph theoretic terminology, Harary [7] and Gallian [8] are newlinereferred. newline Graph labeling [8] is a strong communication between Number theory [6] and newlinestructure of graphs [7] newline The concepts of Total vertex irregular labeling and Edge irregular total K-labeling newlinewere introduced by Baca et.al [2] and also S.Amutha and K.M.Kathiresan have newlineintroduced the notion of Total Edge Fibonnacci Irregular labeling. They have newlineproved some standard graphs. newline The above concepts motivate us to define the following definition newline A total edge Lucas irregular labeling f : V(G) ÈE (G) ® {1,2, ,K} of a graph =( ,!) is a labeling of vertices and edges of G in such a way that for any two different edges quot# and quotand#8242;#and#8242; , their weights $(quot)+$(quot#)+$(#) and $(quotand#8242;)+$(quotand#8242;#and#8242;)+$(#and#8242;) are distinct Lucas numbers where the Lucas series is given by the recurrence relation %and =%andand#8722;1 +%andand#8722;2,andgt 1, L1 = 1, L2 = 3, L3 = 4, L4=7 etc., newlineThe total edge Lucas irregularity strength, tels (G) is defined as the minimum K for newlinewhich G has total edge Lucas irregular labeling. newline