Vertex Sum Cube Labeling for Split and Mirror Graphs

Abstract

In this paper, the new concept vertex sum cube labeling has been introduced and a formula for vertex sum cube labeling has been established. A function is called a Vertex sum cube labeling of a graph with edges, if the vertices of to the set such that when each edge is assigned the label , then the resulting edge labels are distinct cube numbers. In this paper, some families of graphs such as Mirror and Split has been investigated

Introduction

I. INTRODUCTION

A study of points and lines is called graph theory. It is a branch of mathematics concerned with graph analysis. The mathematical truth is depicted visually in this illustration. The link between vertices, or nodes, and edges, or lines, is the subject of graph theory.The study of mathematical structures called graphs, which are made up of vertices (or nodes) connected by edges, is known as graph theory.

Every edge in the set of objects called vertices has an unordered pair of vertices connected with it, as does another set whose members are called edges. The symbols and correspond to the vertex set and edge set of a graph G.G's size, denoted by q, is the cardinality of the edge set, and its order, represented by p, is the cardinality of the vertex set. The new idea of vertex sum cube labeling was presented in this chapter.  This concept is extended to Weiner index polynomial which is cited as [9,10,11,12,14]. Some basic definitions and notations are referred in [1,2,4,5]. Vertex Cube labeling can be applied to different types of graphs which is cited as[13,15,16,17,18,19,20,21,22,23,24,25]. Graph labeling is also extended to domination [3,6,7,8].

Conclusion

In this paper, examines the formula for a vertex sum cube labeling and examines several graph families under this labeling scheme. The conclusion is that some graph families, such split and mirror , are vertex sum cube graphs.

References

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Copyright

Copyright © 2024 P. Shalini, S. Prema. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.