图的双意大利支配数的界

IF 0.5 4区数学 Q3 MATHEMATICS

Discussiones Mathematicae Graph Theory Pub Date : 2022-07-12 DOI:10.7151/dmgt.2330

Farzaneh Azvin, N. J. Rad

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引用次数: 3

摘要

摘要对于图G，一个Roman{3}-dominating函数是函数f:V→ {0，1，2，3}具有这样的性质：对于每个顶点u∈V，如果f（u）∈{0，1}，则f（N[u]）≥3。罗马人的重量{3}-dominating函数是w（f）=f（V）=∑V∈V f（V）的和，以及罗马人的最小权{3}-dominating功能是罗马人{3}-domination数，用γ{R3}（G）表示。本文给出了图的双意大利支配数的一个尖锐下界，并改进了[D.a.Mojdeh和L.Volkmann，Roman{3}-domination（意大利双重统治），离散应用。数学283（2022）555–564]。我们还给出了图的双意大利控制数的广义版本的概率上界，并证明了给定的上界是渐近最佳可能的。

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Bounds on the Double Italian Domination Number of a Graph

Abstract For a graph G, a Roman {3}-dominating function is a function f : V → {0, 1, 2, 3} having the property that for every vertex u ∈ V, if f(u) ∈ {0, 1}, then f(N[u]) ≥ 3. The weight of a Roman {3}-dominating function is the sum w(f) = f(V) = Σv∈V f(v), and the minimum weight of a Roman {3}-dominating function is the Roman {3}-domination number, denoted by γ{R3}(G). In this paper, we present a sharp lower bound for the double Italian domination number of a graph, and improve previous bounds given in [D.A. Mojdeh and L. Volkmann, Roman {3}-domination (double Italian domination), Discrete Appl. Math. 283 (2022) 555–564]. We also present a probabilistic upper bound for a generalized version of double Italian domination number of a graph, and show that the given bound is asymptotically best possible.

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来源期刊

Discussiones Mathematicae Graph Theory MATHEMATICS-

CiteScore

2.20

自引率

0.00%

发文量

审稿时长

53 weeks

期刊介绍： The Discussiones Mathematicae Graph Theory publishes high-quality refereed original papers. Occasionally, very authoritative expository survey articles and notes of exceptional value can be published. The journal is mainly devoted to the following topics in Graph Theory: colourings, partitions (general colourings), hereditary properties, independence and domination, structures in graphs (sets, paths, cycles, etc.), local properties, products of graphs as well as graph algorithms related to these topics.