Edge Irregular Reflexive Labeling for Disjoint Union of Generalized Petersen Graph

• Main Authors: Juan L. G. Guirao, Sarfraz Ahmad, Muhammad Kamran Siddiqui, Muhammad Ibrahim
• Format: Article
• Language: English
• Published: MDPI AG 2018-12-01
• Series: Mathematics
• Subjects: edge irregular reflexive labeling; reflexive edge strength; generalized peterson graphs
• Online Access: https://www.mdpi.com/2227-7390/6/12/304

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 <inline-formula> <math display="inline"> <semantics> <mrow> <mi>G</mi> <mo>=</mo> <mo stretchy="false">(</mo> <mi>V</mi> <mo>,</mo> <mi>E</mi> <mo stretchy="false">)</mo> </mrow> </semantics> </math> </inline-formula> a vertex labeling is a capacity from <i>V</i> 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 <i>E</i> to an arrangement of labels. For this situation, the graph is called an edge-labeled graph. We examine an edge irregular reflexive <i>k</i>-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 <i>s</i> isomorphic duplicates of the cycle related graphs to be specific Generalized Peterson graphs.