Edge Irregular Reflexive Labeling for the Disjoint Union of Gear Graphs and Prism Graphs

Xiujun Zhang, Muhammad Ibrahim, Syed Ahtsham ul Haq Bokhary and Muhammad Kamran Siddiqui
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Xiujun Zhang: School of Information Science and Engineering, Chengdu University, Chengdu 610106, China
Muhammad Ibrahim: Centre for Advanced Studies in Pure and Applied Mathematics, Bahauddin Zakariya University, Multan 60800, Pakistan
Syed Ahtsham ul Haq Bokhary: Centre for Advanced Studies in Pure and Applied Mathematics, Bahauddin Zakariya University, Multan 60800, Pakistan
Muhammad Kamran Siddiqui: Department of Mathematics, COMSATS University Islamabad, Sahiwal Campus, Sahiwal 57000, Pakistan

Mathematics, 2018, vol. 6, issue 9, 1-10

Abstract: In graph theory, a graph is given names—generally a whole number—to edges, vertices, or both in a chart. Formally, given a graph G = ( V , E ) , a vertex naming is a capacity from V to an arrangement of marks. A diagram with such a capacity characterized defined is known as a vertex-marked graph. Similarly, an edge naming is a mapping of an element of E to an arrangement of marks. In this case, the diagram is called an edge-marked graph. We consider an edge irregular reflexive k -labeling for the disjoint association of wheel-related diagrams and deduce the correct estimation of the reflexive edge strength for the disjoint association of m copies of some wheel-related graphs, specifically gear graphs and prism graphs.

Keywords: edge irregular reflexive labeling; reflexive edge strength; gear graphs; prism graphs (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2018
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