**Title:** Characterization and Zagreb indices of the projective path graphs of order *k*

**Montes Taurus J. Pure Appl. Math.** / ISSN: 2687-4814

**Article ID:** MTJPAM-D-22-00042; **Volume 5 / Issue 3 / Year 2023**, Pages 111-119

**Document Type:** Research Paper

**Author(s):** Fatma Özen Erdoğan ^{a}

^{a}Department of Mathematics, Faculty of Arts and Science, Bursa Uludag University, 16059 Bursa, Turkey

Received: 30 December 2022, Accepted: 22 March 2023, Published: 30 March 2023.

**Corresponding Author:** Fatma Özen Erdoğan (Email address: fatmaozen@uludag.edu.tr)

**Full Text:** PDF

**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.

**Keywords:** Graph, degree sequence, path, projective plane, topological indices, energy, spectrum, adjacency matrix

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