SIGNED TOTAL DOUBLE ROMAN DOMINATION NUMBERS IN DIGRAPHS

Let D = (V, A) be a finite simple digraph. A signed total double Roman dominating function (STDRD-function) on the digraph D is a function f : V(D) [right arrow] {- 1,1,2,3} satisfying the following conditions: (i) [Please download the PDF to view the mathematical expression] for each v [member of]...

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Bibliographic Details
Published in:TWMS journal of applied and engineering mathematics 2022-01, Vol.12 (1), p.357
Main Authors: Amjadi, J, Hosseini, F. Pour
Format: Article
Language:English
Subjects:
Graph theory
Mathematical functions
Mathematical research
Minimum weight
Upper bounds
Online Access:Get full text
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Summary:Let D = (V, A) be a finite simple digraph. A signed total double Roman dominating function (STDRD-function) on the digraph D is a function f : V(D) [right arrow] {- 1,1,2,3} satisfying the following conditions: (i) [Please download the PDF to view the mathematical expression] for each v [member of] V(D), where N~ (v) consist of all in-neighbors of v, and (ii) if f(v) = - 1, then the vertex v must have at least two in-neighbors assigned 2 under f or one in-neighbor assigned 3 under f, while if f(v) = 1, then the vertex v must have at least one in-neighbor assigned 2 or 3 under f. The weight of a STDRD-function f is the value [Please download the PDF to view the mathematical expression]. The signed total double Roman domination number (STDRD-number) [Please download the PDF to view the mathematical expression] of a digraph D is the minimum weight of a STDRD-function on D. In this paper we study the STDRD-number of digraphs, and we present lower and upper bounds for [Please download the PDF to view the mathematical expression] in terms of the order, maximum degree and chromatic number of a digraph. In addition, we determine the STDRD-number of some classes of digraphs. Keywords: signed total double Roman dominating function, signed total double Roman domination number, directed graph AMS Subject Classification: 05C69
ISSN:2146-1147
2146-1147