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

Nosheen Goshi, Sohail Zafar, Tabasam Rashid and Juan L. G. Guirao
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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

Mathematics, 2021, vol. 9, issue 19, 1-12

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 ) .

Keywords: edge resolving neighborhood; fractional edge dimension (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
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