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New and improved results on the signed (total) $k$ -domination number of graphs

D. A. Mojdeh

Department of Mathematics, University of Mazandaran, Babolsar, Iran

E-mail Address: damojdeh@umz.ac.ir

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and

Babak Samadi

Department of Mathematics, University of Mazandaran, Babolsar, Iran

E-mail Address: samadibabak62@gmail.com

Corresponding author.

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https://doi.org/10.1142/S1793830917500240Cited by:3 (Source: Crossref)

Abstract

In this paper, we study the signed $k$ -domination and its total version in graphs. By a simple uniform approach we give some new upper and lower bounds on these two parameters of a graph in terms of several different graph parameters. In this way, we can improve and generalize some results in literature. Moreover, we make use of the well-known theorem of Turán [On an extremal problem in graph theory, Math. Fiz. Lapok48 (1941) 436–452] to bound the signed total $k$ -domination number, $γ_{k S}^{t} (G)$ , of a $K_{r + 1}$ -free graph $G$ for $r \geq 2$ .

Keywords:

AMSC: 05C69

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