Bounds on the domination number and the metric dimension of co-normal product of graphs

Imran Javaid; Shahid Ur Rehman; Muhammad Imran

doi:10.1186/s13660-018-1752-5

Bounds on the domination number and the metric dimension of co-normal product of graphs

J Inequal Appl. 2018;2018(1):162. doi: 10.1186/s13660-018-1752-5. Epub 2018 Jul 4.

Authors

Imran Javaid¹, Shahid Ur Rehman¹, Muhammad Imran^{2

3}

Affiliations

¹ 1Centre for Advanced Studies in Pure and Applied Mathematics, Bahauddin Zakariya University, Multan, Pakistan.
² 2Department of Mathematical Sciences, United Arab Emirates University, Al Ain, United Arab Emirates.
³ 3Department of Mathematics, School of Natural Sciences, National University of Sciences and Technology, Islamabad, Pakistan.

Abstract

In this paper, we establish bounds on the domination number and the metric dimension of the co-normal product graph $G_{H}$ of two simple graphs G and H in terms of parameters associated with G and H. We also give conditions on the graphs G and H for which the domination number of $G_{H}$ is 1, 2, and the domination number of G. Moreover, we give formulas for the metric dimension of the co-normal product $G_{H}$ of some families of graphs G and H as a function of associated parameters of G and H.

Keywords: Adjacency resolving set; Co-normal product of graphs; Dominating set; Resolving set.