TY - JOUR
AU - Varughese Mathew,
AU - Ansmol George,
PY - 2020/03/15
Y2 - 2024/02/23
TI - The Minimum Resolving Energy of a Graph
JF - International Journal of Mathematics And its Applications
JA - Int. J. Math. And Appl.
VL - 8
IS - 1
SE - Research Article
DO -
UR - http://ijmaa.in/index.php/ijmaa/article/view/196
SP - 239-246
AB - <p>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.</p>
ER -