Lehmer-3 mean labeling of graphs

Abstract

A graph G=(V,E) with P vertices and q edges is called Lehmer-3 mean graph, if it is possible to label vertices x Є V with distinct label f(x) from 1,2,3,………….q+1 in such a way that when each edge e=uv is labeled with f(e=uv)=⌈ f(u) 3 +f(v) 3 f(u) 2 +f(v) 2 ⌉ (or) ⌊ f(u) 3 +f(v) 3 f(u) 2 +f(v) 2 ⌋, then the edge labels are distinct. In this case f is called Lehmer-3 mean labeling of G. In this paper we investigate Lehmer-3 mean labeling of some standard graphs.

k- Super Lehmer-3 Mean Graphs

“…If it is possible to label vertices x ЄV with distinct labels f(x) from 1,2,3,………….q+1 in such a way that when each edge e=uv is labeled with f(e=uv)= 2 , then the edge labels are distinct. In this case "f " is called Lehmer -3 mean labeling of G.…”

“…For standerd terminology and notations we follow Harrary [1]. S Somasundaram & S.S Sandhya introduced the concept of Harmonic Mean Labeling of Graphs in [2] and its basic results was proved in [3] and [4].We will provide a brief summary of other informations which are necessary for our present investigation.…”

Some New Graphs on k-Super Mean Labeling

“…Particularly interesting applications of graph theory can be found in [1][2][3][4]. The concept of mean labeling was introduced and studied by S. Somasundaram and R. Ponraj [12]. The concept of super mean labeling was introduced and studied by D. Ramya et al [11].…”

Degree Splitting of Heronian Mean Graphs

“…For all other standard terminology and notations we follow Harary (Harary, 1988). The concept of Mean labeling was introduced in (Somasundaram & Ponraj, 2003). The concept of Harmonic Mean labeling was introduced in (Somasundaram, Ponraj, & Sandhya).…”