Edge Irregular Reflexive Labeling for Disjoint Union of Generalized Petersen Graph

Abstract

A graph labeling is the task of integers, generally spoken to by whole numbers, to the edges or vertices, or both of a graph. Formally, given a graph G = ( V , E ) a vertex labeling is a capacity from V to an arrangement of integers. A graph with such a capacity characterized is known as a vertex-labeled graph. Similarly, an edge labeling is an element of E to an arrangement of labels. For this situation, the graph is called an edge-labeled graph. We examine an edge irregular reflexive k-labeling for the disjoint association of the cycle related graphs and decide the correct estimation of the reflexive edge strength for the disjoint association of s isomorphic duplicates of the cycle related graphs to be specific Generalized Peterson graphs.

On H-irregular reflexive labeling of graph

“…The formal definition of vertex irregular reflexive 𝑘-labeling can be seen in [7,8]; they also provided some results on 𝑟𝑣𝑠(𝐺), the smallest value of 𝑘 for which such labeling exists is called the reflexive vertex strength of the graph 𝐺, where 𝐺 were prisms, wheels, fans, baskets, any graph with pendant vertex, sunlet graph, helm graph, subdivided star graph, and broom graph. While for a formal definition of edge irregular reflexive 𝑘-labeling can be seen in [8,9,10,11,12,13,14,15]. They determined the lower bound lemma and some previous results of 𝑟𝑒𝑠(𝐺), where 𝐺 were a star, double star 𝑆 𝑛,𝑛 , caterpillar graphs, generalized subdivided star, broom, double star graph 𝑆 𝑛,𝑚 , cycle, a cartesian product of cycles, join of cycle graphs and 𝐾 1 , generalized friendship graphs, wheels, prisms, basket, and fan graphs, the disjoint union of Generalized Petersen graphs.…”

Edge Irregular Reflexive Labeling for Some Classes of Plane Graphs

“…Bača et al [1] studied the exact value of the reflexive edge strength for cycles, Cartesian product of two cycles and for join graphs of the path and cycle with 2K 2 . In [5], the authors investigated the exact value of the reflexive edge strength for disjoint union of s isomorphic copies of generalized Peterson graphs. Tanna et al [8] determined the exact value of the reflexive edge strength for prisms and wheels.…”

“…[5,10] Any graph G with maximum degree ∆(G) satisfies: where r = 1 for |E(G)| ≡ 2, 3(mod 6), and zero otherwise.…”

The reflexive edge strength on some almost regular graphs

“…J.L.G. Guirao et al in [17] determined the , where G was the disjoint union of Generalized Petersen graphs. In this paper we will study the reflexive edge strength on graphs with a specific property, namely almost regular graphs.…”