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

Author

Listed:
  • 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)

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.

Suggested Citation

  • Xiujun Zhang & Muhammad Ibrahim & Syed Ahtsham ul Haq Bokhary & Muhammad Kamran Siddiqui, 2018. "Edge Irregular Reflexive Labeling for the Disjoint Union of Gear Graphs and Prism Graphs," Mathematics, MDPI, vol. 6(9), pages 1-10, August.
    • Handle: RePEc:gam:jmathe:v:6:y:2018:i:9:p:142-:d:164988
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    References listed on IDEAS

    as
    1. Muhammad Kamran Siddiqui & Deeba Afzal & Muhammad Ramzan Faisal, 2017. "Total edge irregularity strength of accordion graphs," Journal of Combinatorial Optimization, Springer, vol. 34(2), pages 534-544, August.
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