K-metric antidimension of some generalized petersen graphs

Abstract

Resistance of social graphs to active attacks is a very important feature which must be maintained in the modern networks. Recently introduced k-metric antidimension graph invariant is used to define a new measure for resistance of social graphs. In this paper we have found and proved the k-metric antidimension for generalized Petersen graphs GP(n, 1) and GP(n, 2). It is proven that GP(2m+1, 1) and GP(8, 2) are 2-metric antidimensional, while all other GP(n, 1) and GP(n, 2) graphs are 3-metric antidimensional.