Study of some New labeling Techniques and Energy of Graphs

Abstract

Abstract newline newline newlineChapter - 1: Introduction newlineThis chapter contains a brief introduction of Basics of Graph Theory, Graph labeling and Energy of Graph. newlineChapter - 2: Preliminaries newlineThis chapter contains a brief introduction of basic definitions and preliminaries needed for the subsequent chapters. newlineChapter - 3: Some Harmonic Mean Cordial Graphs newlineLet G = (V(G),E(G)) be a simple undirected Graph. A function and#8200;fand#8200;:and#8200;V(G)and#8200;and#8594;and#8200;\{1,2\} is called Harmonic Mean Cordial if the induced function f^*:E(G)and#8594;\{1,2\} defined by f^* (uv)=and#8970;2f(u)f(v)/(f(u)+f(v) )and#8971; satisfies the condition |v_f (i)-v_f (j)|and#8804;1 and |e_f (i)-e_f (j)|and#8804;1 for any i,j and#8712;\{1,2\}, where v_f (x) and e_f (x) denotes the number of vertices and number of edges with label x respectively and and#8970;xand#8971; denotes the greatest integer less than or equals to x. A Graph G is called Harmonic Mean Cordial Graph if it admits Harmonic Mean Cordial labeling. This chapter contains some harmonic mean cordial labeling of some interesting graphs. newlineChapter - 4: Some Non-Harmonic Mean Cordial Graphs newlineLet G=(V(G),E(G)) be a simple undirected Graph is called Non-Harmonic Mean Cordial Graph if it does not admit Harmonic Mean Cordial labeling. This chapter contains some non-harmonic mean cordial labeling of some interesting graphs. newlineChapter - 5: Results on Energy of Graphs newlineThe eigenvalue of a graph G is the eigenvalue of its adjacency matrix. The energy E(G) of G is the sum of absolute values of its eigenvalues. This chapter contains some results on energies of graph for K_mand#8744;K_n. newline newline