Results 11 to 20 of about 437 (67)
On the signed total Roman domination and domatic numbers of graphs
Discrete Applied Mathematics, 2016 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Lutz Volkmann
exaly +4 more sources
On the signed strong total Roman domination number of graphs
Tamkang Journal of Mathematics, 2022 Let $G=(V,E)$ be a finite and simple graph of order $n$ and maximumdegree $\Delta$. A signed strong total Roman dominating function ona graph $G$ is a function $f:V(G)\rightarrow\{-1, 1,2,\ldots, \lceil\frac{\Delta}{2}\rceil+1\}$ satisfying the condition that (i) forevery vertex $v$ of $G$, $f(N(v))=\sum_{u\in N(v)}f(u)\geq 1$, where$N(v)$ is the open ...
Mahmoodi, A., Atapour, M., Norouzian, S.
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Signed double Roman domination on cubic graphs [PDF]
Applied Mathematics and Computation, 2023 The signed double Roman domination problem is a combinatorial optimization problem on a graph asking to assign a label from $\{\pm{}1,2,3\}$ to each vertex feasibly, such that the total sum of assigned labels is minimized.
E. Iurlano +3 more
semanticscholar +5 more sources
Several Roman domination graph invariants on Kneser graphs [PDF]
Discrete Mathematics & Theoretical Computer Science, 2022 This paper considers the following three Roman domination graph invariants on Kneser graphs: Roman domination, total Roman domination, and signed Roman domination. For Kneser graph $K_{n,k}$, we present exact values for Roman domination number $\gamma_{
Tatjana Zec, Milana Grbi'c
semanticscholar +3 more sources
Signed total Roman domination in graphs
Journal of combinatorial optimization, 2016 Let $$G$$G be a finite and simple graph with vertex set $$V(G)$$V(G). A signed total Roman dominating function (STRDF) on a graph $$G$$G is a function $$f:V(G)\rightarrow \{-1,1,2\}$$f:V(G)→{-1,1,2} satisfying the conditions that (i) $$\sum _{x\in N(v)}f(
L. Volkmann
semanticscholar +2 more sources
The Signed Total Mixed Roman Domination Numbers of Graphs
Journal of Physics: Conference SeriesAbstract The problem of signed domination of graphs is a typical optimization problem. It requires that each vertex and edge be assigned a feasible label so that the sum of assigned labels is minimized. First, we propose the concept of a signed total mixed Roman domination number and introduce the related research progress.
Xia Hong, Li Zhang, Xiaobing Guo
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Relating the Outer-Independent Total Roman Domination Number with Some Classical Parameters of Graphs [PDF]
Mediterranean Journal of Mathematics, 2022 For a given graph G without isolated vertex we consider a function f:V(G)→{0,1,2}\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage ...
A. Cabrera Martínez +2 more
semanticscholar +2 more sources
The signed (total) Roman domination problem on some classes of planar graphs - Convex polytopes [PDF]
Discret. Math. Algorithms Appl., 2021 In this paper we deal with the calculation of the signed (total) Roman domination numbers, $\gamma_{sR}$ and $\gamma_{stR}$ respectively, on a few classes of planar graphs from the literature.
Tatjana Zec +2 more
semanticscholar +1 more source
Signed Total Strong Roman Domination in Graphs
Discrete Mathematics Letters, 2022 Let G = ( V, E ) be a finite and simple graph of order n and maximum degree ∆ . A signed total strong Roman dominating function on G is a function f : V → {− 1 , 1 , 2 , . . .
M. Hajjari, S. Sheikholeslami
semanticscholar +1 more source
Closed formulas for the total Roman domination number of lexicographic product graphs
Ars Math. Contemp., 2021 Let G be a graph with no isolated vertex and f : V ( G ) → {0, 1, 2} a function. Let V i = { x ∈ V ( G ) : f ( x ) = i } for every i ∈ {0, 1, 2} . We say that f is a total Roman dominating function on G if every vertex in V 0 is adjacent to at least
Abel Cabrera Martínez +1 more
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