The Minimum Resolving Energy of a Graph

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  • Varughese Mathew Department of Mathematics, Mar Thoma College Tiruvalla, Kerala, India
  • Ansmol George Department of Mathematics, Bishop Chulaparambil Memorial College, Kottayam, Kerala, India


Minimum resolving set, metric dimension, minimum resolving matrix, minimum resolving eigenvalue, minimum resolving energy of a graph


A subset $W$ of vertrices in a connected graph $G=(V,E)$ is called a resolving set of $G$ if all other vertices are uniquely determined by their distances in $W.$ The metric dimension $dim(G)$ of a graph $G$ is the minimum cardinality of a resolving set of $G.$ In this paper, for a minimum resolving set $R$ of a graph $G,$ we define the minimum resolving energy $E_R(G)$ of $G.$ We study this parameter for some standard graphs. Some properties of $E_R(G)$ and bounds were also obtained.




How to Cite

Varughese Mathew, & Ansmol George. (2020). The Minimum Resolving Energy of a Graph. International Journal of Mathematics And Its Applications, 8(1), 239–246. Retrieved from



Research Article