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.