doiSerbia

K-metric antidimension of some generalized Petersen graphs

Kratica Jozef (Mathematical Institute, Serbian Academy of Sciences and Arts, Belgrade, Serbia)
Kovačević-Vujčić Vera (Faculty of Organizational Sciences, University of Belgrade, Belgrade, Serbia)
Čangalović Mirjana (Faculty of Organizational Sciences, University of Belgrade, Belgrade, Serbia)

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 anew 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.

Keywords: Generalized Petersen graphs, k-metric antidimension, Graph theory

Projects of the Serbian Ministry of Education, Science and Technological Development, Grant no. 174010 and Grant no. 174033