Results 11 to 20 of about 4,628 (221)

On the outer-independent {2}-domination in rooted product graphs

Open Mathematics
Let G be a graph with vertex set V(G). A function f: V(G) → {0, 1, 2} is called an outer-independent {2}-dominating function on G if ∑ u∈N[v] f(u) ≥ 2 for every vertex v ∈ V(G) and {v ∈ V(G) : f(v) = 0} is an independent set of G. The minimum weight ω(f)
Cabrera-Martínez Abel, Conchado-Peiró Andrea, Rodríguez José M.   +2 more
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Italian Domination in Rooted Product Graphs [PDF]

Bulletin of the Malaysian Mathematical Sciences Society, 2020
In this article, we obtain closed formulae for the Italian domination number of rooted product graphs. As a particular case of the study, we derive the corresponding formulas for corona graphs, and we provide an alternative proof that the problem of computing the Italian domination number of a graph is NP-hard.
R. Hernández-Ortiz, L. P. Montejano, J. A. Rodríguez-Velázquez   +2 more
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Roman domination in direct product graphs and rooted product graphs

AIMS Mathematics, 2021
<abstract><p>Let $ G $ be a graph with vertex set $ V(G) $. A function $ f:V(G)\rightarrow \{0, 1, 2\} $ is a Roman dominating function on $ G $ if every vertex $ v\in V(G) $ for which $ f(v) = 0 $ is adjacent to at least one vertex $ u\in V(G) $ such that $ f(u) = 2 $. The Roman domination number of $ G $ is the minimum weight $ \omega(f) =
Cabrera Martínez, Abel, Peterin, Iztok, González Yero, Isamel   +2 more
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Spectra of M-edge rooted product of graphs

Indian Journal of Pure and Applied Mathematics, 2021
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
R. Pavithra, R. Rajkumar
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Domination-Related Parameters in Rooted Product Graphs [PDF]

Bulletin of the Malaysian Mathematical Sciences Society, 2015
A set $S$ of vertices of a graph $G$ is a dominating set in $G$ if every vertex outside of $S$ is adjacent to at least one vertex belonging to $S$. A domination parameter of $G$ is related to those sets of vertices of a graph satisfying some domination property together with other conditions on the vertices of $G$.
Kuziak, Dorota, Lemańska, Magdalena, Yero, Ismael G.   +2 more
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Strong metric dimension of rooted product graphs [PDF]

International Journal of Computer Mathematics, 2015
16 pages.
Dorota Kuziak, Ismael González Yero, Juan A. Rodríguez-Velázquez   +2 more
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VERTEX-ECCENTRICITY DESCRIPTORS IN DENDRIMERS

Studia Universitatis Babes-Bolyai Chemia, 2017
In this paper, we present graph theoretical methods to compute several vertex-eccentricity-based molecular descriptors such as the eccentric connectivity index, total eccentricity, average eccentricity and first and second Zagreb eccentricity indices ...
Mahdieh AZARI, Ali IRANMANESH, Mircea V. DIUDEA   +2 more
doaj   +1 more source

The general position problem and strong resolving graphs

Open Mathematics, 2019
The general position number gp(G) of a connected graph G is the cardinality of a largest set S of vertices such that no three pairwise distinct vertices from S lie on a common geodesic.
Klavžar Sandi, Yero Ismael G.
doaj   +1 more source

Equitable Coloring On Rooted Product Of Graphs

Turkish Journal of Computer and Mathematics Education (TURCOMAT), 2021
A finite and simple graph  is said to be equitably  colorable if its vertices can be partitioned into  classes  such that each  is an independent set and  holds for every . The smallest integer  for which  is equitable chromatic number of  and denoted by .
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Computing the Metric Dimension of a Graph from Primary Subgraphs

Discussiones Mathematicae Graph Theory, 2017
Let G be a connected graph. Given an ordered set W = {w1, . . . , wk} ⊆ V (G) and a vertex u ∈ V (G), the representation of u with respect to W is the ordered k-tuple (d(u, w1), d(u, w2), . . .
Kuziak Dorota, Rodríguez-Velázquez Juan A., Yero Ismael G.   +2 more
doaj   +1 more source