On the edge metric dimension and Wiener index of the blow up of graphs
Abstract
Let
be a connected graph. The distance between an edge
and a vertex
is defined as
A nonempty set
is an edge metric generator for
if for any two distinct edges
, there exists a vertex
such that
. An edge metric generating set with the smallest number of elements is called an edge metric basis of
, and the number of elements in an edge metric basis is called the edge metric dimension of
and it is denoted by
. In this paper, we study the edge metric dimension of a blow up of a graph
, and also we study the edge metric dimension of the zero divisor graph of the ring of integers modulo
. Moreover, the Wiener index and the hyper-Wiener index of the blow up of certain graphs are computed.














DOI Code:
10.1285/i15900932v40n2p99
Keywords:
Edge metric dimension; Wiener index; Hyper-Wiener index; Blow up of a graph; Zero divisor graph
Full Text: PDF