Signed total Roman domination in graphs

Volkmann, Lutz

doi:10.1007/s10878-015-9906-6

Cited by 25 publications

(22 citation statements)

References 7 publications

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“…Corollary 2.4. ( [1,14]) Let G be a graph of order n, minimum degree δ and maximum degree ∆. If δ < ∆, then…”

Section: Corollary 23mentioning

confidence: 99%

“…In this paper, we continue the study of signed Roman domination in graphs and digraphs (see, for example, [1,2,3,4,7,8,9,10,11,12,13,14]).…”

mentioning

confidence: 99%

“…Let K n and D(K n ) be the complete graph and complete digraph of order n, respectively. In [14], the author determines the weak signed Roman domination number of complete graphs. Using Observation 1.1 and Proposition 1.1 , we obtain the weak signed Roman domination number of complete digraphs.…”

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confidence: 99%

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Weak Signed Roman Domination in Digraphs

Volkmann

2021

Tamkang J. Math.

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Let $D$ be a finite and simple digraph with vertex set $V(D)$. A weak signed Roman dominating function (WSRDF) on a digraph $D$ is a function $f:V(D)\rightarrow\{-1,1,2\}$ satisfying the condition that $\sum_{x\in N^-[v]}f(x)\ge 1$ for each $v\in V(D)$, where $N^-[v]$ consists of $v$ and allvertices of $D$ from which arcs go into $v$. The weight of a WSRDF $f$ is $\sum_{v\in V(D)}f(v)$. The weak signed Roman domination number $\gamma_{wsR}(D)$ of $D$ is the minimum weight of a WSRDF on $D$. In this paper we initiate the study of the weak signed Roman domination number of digraphs, and we present different bounds on $\gamma_{wsR}(D)$. In addition, we determine the weak signed Roman domination number of some classesof digraphs.

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“…Corollary 2.4. ( [1,14]) Let G be a graph of order n, minimum degree δ and maximum degree ∆. If δ < ∆, then…”

Section: Corollary 23mentioning

confidence: 99%

“…In this paper, we continue the study of signed Roman domination in graphs and digraphs (see, for example, [1,2,3,4,7,8,9,10,11,12,13,14]).…”

mentioning

confidence: 99%

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Weak Signed Roman Domination in Digraphs

Volkmann

2021

Tamkang J. Math.

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“…Total roman domination which is suggested by the article in "Total Roman domination in graphs" by Ahangar, Henning, Samodivkin & Yero [2]. Volkmann [3,4] introduced the concept of signed total roman domination in graphs.…”

Section: G Gmentioning

confidence: 99%

Signed Total Roman Dominating Functions of Corona Product of a Path with a Complete Graph

Rani¹,

Begum²,

Raju³

et al. 2017

IJMTT

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Graph theory is a fascinating subject in mathematics. Its Applications in many fields like Physical Sciences, Engineering communications, coding theory, Linguistics, Logical Algebra and Computer networking. Let G be a simple graph with vertex set V and edge set E and the function : [0,1] fV  is called a dominating function (DF) of G, if for each vV  , the sum of the function values over v and the elements incident to v is greater than or equal to one. It is a minimal dominating function (MDF), if for all gf  , g is not DF. In this paper, we study the minimal total dominating functions, minimal total roman dominating functions, minimal signed total roman dominating functions of corona product graph of a path with a complete graph and obtain total domination number () t G  , total roman domination number () tR G  and signed total roman domination number () stR G  of these graphs.

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“…Since then, a lot of papers have been published on various aspects of Roman domination [3,4] and many variations [5][6][7]. Italian domination is a new variation of Roman domination.…”

Section: Introductionmentioning

confidence: 99%

The Italian Domination Numbers of Generalized Petersen Graphs P(n,3)

Gao

et al. 2019

Mathematics

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An Italian dominating function of G is a function f : V ( G ) → { 0 , 1 , 2 } , for every vertex v such that f ( v ) = 0 , it holds that ∑ u ∈ N ( v ) f ( u ) ≥ 2 . The Italian domination number γ I ( G ) is the minimum weight of an Italian dominating function on G. In this paper, we determine the exact values of the Italian domination numbers of P ( n , 3 ) .

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Signed total Roman domination in graphs

Abstract: Let G be a finite and simple graph with vertex set

Cited by 25 publications

References 7 publications

Weak Signed Roman Domination in Digraphs

Weak Signed Roman Domination in Digraphs

Signed Total Roman Dominating Functions of Corona Product of a Path with a Complete Graph

The Italian Domination Numbers of Generalized Petersen Graphs P(n,3)

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