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A Combinatorial Approach to the Computation of the Fractional Edge Dimension of Graphs

Author

Listed:
  • Nosheen Goshi

    (Department of Mathematics, University of Management and Technology, Lahore 54770, Pakistan)

  • Sohail Zafar

    (Department of Mathematics, University of Management and Technology, Lahore 54770, Pakistan)

  • Tabasam Rashid

    (Department of Mathematics, University of Management and Technology, Lahore 54770, Pakistan)

  • Juan L. G. Guirao

    (Departamento de Matematica Aplicada y Estadistica, Universidad Politecnica de Cartagena, 30202 Cartagena, Spain
    Nonlinear Analysis and Applied Mathematics (NAAM)-Research Group, Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia)

Abstract

E. Yi recently introduced the fractional edge dimension of graphs. It has many applications in different areas of computer science such as in sensor networking, intelligent systems, optimization, and robot navigation. In this paper, the fractional edge dimension of vertex and edge transitive graphs is calculated. The class of hypercube graph Q n with an odd number of vertices n is discussed. We propose the combinatorial criterion for the calculation of the fractional edge dimension of a graph, and hence applied it to calculate the fractional edge dimension of the friendship graph F k and the class of circulant graph C n ( 1 , 2 ) .

Suggested Citation

  • Nosheen Goshi & Sohail Zafar & Tabasam Rashid & Juan L. G. Guirao, 2021. "A Combinatorial Approach to the Computation of the Fractional Edge Dimension of Graphs," Mathematics, MDPI, vol. 9(19), pages 1-12, September.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:19:p:2364-:d:641687
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