Authors : K.L. Bhavyavenu and Venkanagouda M. Goudar
Abstract: In this study, we study the concept of doubly connected geodetic number of a graph. A set SfV in a graph G is a Doubly Connected Geodetic Set [DCGS] if S is a geodetic set and both induced subgraphs < S > and < V-S > are connected. The minimum cardinality of a doubly connected geodetic set and it is denoted by gdc (G) is called doubly connected geodetic number of a graph G. A doubly connected geodetic set of cardinality gdc (G) is called gdc (G)-set. We determine the doubly connected geodetic number in cartesian product, strong product, join of two graphs
K.L. Bhavyavenu and Venkanagouda M. Goudar, 2018. Doubly Connected Geodetic Number on Operations in Graphs. Journal of Engineering and Applied Sciences, 13: 4330-4335.