MVLSC Home · Issue Contents · Forthcoming Papers
Wiener Energies of Fuzzy Graphs
Uzma Ahmad, Imdad Hussain and A. Borumand Saeid
The topological indices and energies for fuzzy graphs are worthwhile in various multi-criteria decision making (MCDM) problems due to its connectivity-based formulation. Mostly, the value of topological index of a fuzzy graph is based on different parameters, like fuzzy edge or vertex membership, fuzzy distance or fuzzy degrees, etc. The focus of this paper is to extend the concept of energy of fuzzy graph to a topological index (Wiener index) based energy of fuzzy graph. For this, fuzzy Wiener matrix, fuzzyWiener Laplacian matrix and corresponding Wiener based energies of fuzzy graphs are defined. A bound on largest eigenvalue of fuzzy Wiener matrix is estimated. Several results related to eigenvalues of fuzzy Wiener and fuzzy Wiener Laplacian matrices are proved. Several upper and lower bounds for energies of these matrices are also established in terms of parameters, like number of vertices, edges, minimum and maximum vertex membership, edge membership, etc. Finally, the idea of fuzzy Wiener energy is applied to a MCDM problem of choosing best organizations based on implementation of total quality management (TQM) attributes.
Keywords: Fuzzy graph, Wiener index, sum distance, Laplacian matrix, eigenvalues, graph energy
AMS(MSC): 03B52, 05C50, 05C09