Signed star k-subdomination numbers in graphs

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Abstract

Let G be a simple graph without isolated vertex with vertex set V (G) and edge set E (G). A function f : E (G) {long rightwards arrow} {- 1, 1} is said to be a signed star k-subdominating function of G if ∑e ∈ E (v) f (e) ≥ 1 for at least k vertices v of G, where E (v) = {u v ∈ E (G) {divides} u ∈ N (v)}. The value min ∑e ∈ E (G) f (e), taking over all signed star k-subdominating function f of G is called the signed star k-subdomination number of G and denoted by γS Sk (G). In this paper we give some bounds on the signed star k-subdomination number of graphs. © 2008 Elsevier B.V. All rights reserved.

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Saei, R., & Sheikholeslami, S. M. (2008). Signed star k-subdomination numbers in graphs. Discrete Applied Mathematics, 156(15), 3066–3070. https://doi.org/10.1016/j.dam.2008.01.020

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