Characterization and Zagreb indices of the projective path graphs of order k

Abstract

In this paper; general formulae for vertex and edge partition of projective path graphs are obtained from projective planes of order k. Then, the characterization of projective-path graphs is presented. The general formulae of additive and multiplicative Zagreb indices and Narumi-Katayama index for the projective path graphs in terms of order k are given. Finally, the vertex-adjacency matrices and energies related to projective path graphs, that are obtained from the projective planes of order k = 2, 3, 4, 5 are calculated.