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

Imran Javaid; Shahid 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

Imran Javaid
, Shahid Rehman
, Muhammad Imran

Department of Mathematical Sciences

Research output: Contribution to journal › Article › peer-review

3 Citations (Scopus)

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.

Original language	English
Article number	162
Journal	Journal of Inequalities and Applications
Volume	2018
DOIs	https://doi.org/10.1186/s13660-018-1752-5
Publication status	Published - 2018

Keywords

Adjacency resolving set
Co-normal product of graphs
Dominating set
Resolving set

ASJC Scopus subject areas

Analysis
Discrete Mathematics and Combinatorics
Applied Mathematics

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10.1186/s13660-018-1752-5

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abstract = "In this paper, we establish bounds on the domination number and the metric dimension of the co-normal product graph GH 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 GH is 1, 2, and the domination number of G. Moreover, we give formulas for the metric dimension of the co-normal product GH of some families of graphs G and H as a function of associated parameters of G and H.",

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AU - Rehman, Shahid

AU - Imran, Muhammad

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AB - In this paper, we establish bounds on the domination number and the metric dimension of the co-normal product graph GH 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 GH is 1, 2, and the domination number of G. Moreover, we give formulas for the metric dimension of the co-normal product GH of some families of graphs G and H as a function of associated parameters of G and H.

KW - Adjacency resolving set

KW - Co-normal product of graphs

KW - Dominating set

KW - Resolving set

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JO - Journal of Inequalities and Applications

JF - Journal of Inequalities and Applications

M1 - 162

ER -

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

Abstract

Keywords

ASJC Scopus subject areas

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