A graph labeling is an assignment of integers to the vertices or edges, or both, subject to
certain conditions. Graph labelings were first introduced in the mid 1960s. In the intervening …

Let G be a connected, simple, and undirected graph with a vertex set V (G) and an edge set
E (G). Total k-labeling is a function fe from the edge set to the first ke natural number, and a …

Graph labeling is an assignment of (usually) positive integers to elements of a graph
(vertices and/or edges) satisfying certain condition (s). In the last two decades, graph …

In computer science, graphs are used in variety of applications directly or indirectly.
Especially quantitative labeled graphs have played a vital role in computational linguistics …

For a simple graph G, a vertex labeling φ: V (G)→{1, 2,..., k} is called a vertex k-labeling. The
weight of an edge xy in G, denoted by wϕ (xy), is the sum of the labels of end vertices x and …

For a graph G=(V, E) we define a labeling ψ: V (G)→{1, 2,···, k} to be a vertex irregular k-
labeling. A vertex irregular k-labeling is defined to be an edge irregular k-labeling of the …

For a simple graph G, a vertex labeling ϕ: V (G)→{1, 2,…, k} is called a vertex k-labeling. For
any edge xy in G, its weight w ϕ (xy)= ϕ (x)+ ϕ (y). If all the edge weights are distinct, then ϕ …

An edge irregular total k-labeling on simple and undirected graph G (V, E) is a map f: V∪
E→{1, 2,…, k} such that for any different edge xy and x′ y′ their weights f (x)+ f (xy)+ f (y) …

Let G be a simple graph with vertex set V (G) and edge set E (G), respectively. An edge
irregular k-labeling of G is a labeling of V (G) with labels from the set {1, 2,…, k} in such a …

Let G be a connected, simple and undirected graph with vertex set V (G) and edge set E (G).
By a labeling we mean any map** that maps a set of graph elements to a set of numbers …