Share This Article:

The Signed Domination Number of Cartesian Product of Two Paths

Full-Text HTML XML Download Download as PDF (Size:2894KB) PP. 45-55
DOI: 10.4236/ojdm.2020.102005    164 Downloads   361 Views

ABSTRACT

Let G be a finite connected simple graph with vertex set V(G) and edge set E(G). A function f:V(G) → {1,1} is a signed dominating function if for every vertex vV(G), the closed neighborhood of v contains more vertices with function values 1 than with 1. The signed domination number γs(G) of G is the minimum weight of a signed dominating function on G. In this paper, we calculate The signed domination numbers of the Cartesian product of two paths Pm and Pn for m = 3, 4, 5 and arbitrary n.

Cite this paper

Hassan, M. , Al Hassan, M. and Mostafa, M. (2020) The Signed Domination Number of Cartesian Product of Two Paths. Open Journal of Discrete Mathematics, 10, 45-55. doi: 10.4236/ojdm.2020.102005.

Copyright © 2020 by authors and Scientific Research Publishing Inc.

Creative Commons License

This work and the related PDF file are licensed under a Creative Commons Attribution 4.0 International License.