Results 21 to 30 of about 133,073 (208)

On the resolving strong domination number of graphs: a new notion

Journal of Physics: Conference Series, 2021
Abstract The study of metric dimension of graph G has widely given some results and contribution of graph research of interest, including the domination set theory. The dominating set theory has been quickly growing and there are a lot of natural extension of this study, such as vertex domination, edge domination, total domination, power
null Dafik, null Slamin, Ika Hesti Agustin, Dwi Agustin Retnowardani, Elsa Yuli Kurniawati   +4 more
openaire   +1 more source

A Comparison between the Zero Forcing Number and the Strong Metric Dimension of Graphs [PDF]

, 2014
The \emph{zero forcing number}, $Z(G)$, of a graph $G$ is the minimum cardinality of a set $S$ of black vertices (whereas vertices in $V(G)-S$ are colored white) such that $V(G)$ is turned black after finitely many applications of "the color-change rule":
A Sebö, CJ Edholm, CX Kang, CX Kang, D Burgarth, D Burgarth, DD Row, E Yi, F Barioli, F Barioli, F Harary, G Chartrand, K Chilakamarri, L Eroh, L Hogben, MR Garey, OR Oellermann, PJ Slater, S Khuller, S Severini   +19 more
core   +1 more source

Strong resolving graph of the intersection graph in commutative rings

, 2023
The intersection graph of ideals associated with a commutative unitary ring $R$ is the graph $G(R)$ whose vertices all non-trivial ideals of $R$ and there exists an edge between distinct vertices if and only if the intersection of them is non-zero. In this paper, the structure of the resolving graph of $G(R)$ is characterized and as an application, we ...
Dodongeh, E., Moussavi, A., Nikandish, R.   +2 more
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Strong Resolving Domination in the Lexicographic Product of Graphs

European Journal of Pure and Applied Mathematics, 2023
Let G be a connected graph. A subset S ⊆ V (G) is a strong resolving dominating set of G if S is a dominating set and for every pair of vertices u, v ∈ V (G), there exists a vertex w ∈ S such that u ∈ IG[v, w] or IG[u, w]. The smallest cardinality of a strong resolving dominating set of G is called the strong resolving domination number of G.
Gerald Bacon Monsanto, Penelyn L. Acal, Helen M. Rara   +2 more
openaire   +1 more source

On 1-movable Strong Resolving Hop Domination in Graphs

European Journal of Pure and Applied Mathematics, 2023
A set S is a 1-movable strong resolving hop dominating set of G if for every v ∈ S, either S\{v} is a strong resolving hop dominating set or there exists a vertex u ∈ (V (G)\S)∩NG(v) such that (S \ {v}) ∩ {u} is a strong resolving hop dominating set of G.
Armalene Abragan, Helen M. Rara
openaire   +1 more source

3/2 Firefighters are not enough [PDF]

, 2010
The firefighter problem is a monotone dynamic process in graphs that can be viewed as modeling the use of a limited supply of vaccinations to stop the spread of an epidemic.
Berlekamp, Bowditch, Develin, Finbow, Finbow, Gács, Hartnell, King, Kloster, MacGillivray, Messinger, Messinger, Máthé, Ng, Ohad N. Feldheim, Rani Hod, Wang   +16 more
core   +1 more source

On the Metric Dimension of Cartesian Products of Graphs [PDF]

, 2005
A set S of vertices in a graph G resolves G if every vertex is uniquely determined by its vector of distances to the vertices in S. The metric dimension of G is the minimum cardinality of a resolving set of G.
Brigham R. C., Carlos Seara, Carmen Hernando, Chartrand G., Chartrand G., Currie J., David R. Wood, Erdo˝s P., Goddard W., Goddard W., Greenwell D. L., Harary F., Ignacio M. Pelayo, José Cáceres, Knuth D. E., Lindström B., Lindström B., María L. Puertas, Mercè Mora, Peters‐Fransen J., Poisson C., Saenpholphat V., Shanmukha B., Slater P. J., Slater P. J., Sooryanarayana B., Sooryanarayana B., Yushmanov S. V.   +27 more
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On the strong metric dimension of the strong products of graphs

Open Mathematics, 2015
Let G be a connected graph. A vertex w ∈ V.G/ strongly resolves two vertices u,v ∈ V.G/ if there exists some shortest u-w path containing v or some shortest v-w path containing u.
Kuziak Dorota, Yero Ismael G., Rodríguez-Velázquez Juan A.   +2 more
doaj   +1 more source

On Strong Resolving Domination in the Join and Corona of Graphs

European Journal of Pure and Applied Mathematics, 2020
Let G be a connected graph. A subset S \subseteq V(G) is a strong resolving dominating set of G if S is a dominating set and for every pair of vertices u,v \in V(G), there exists a vertex w \in S such that u \in I_G[v,w] or v \in I_G[u,w]. The smallest cardinality of a strong resolving dominating set of G is called the strong resolving domination ...
Gerald Bacon Monsanto, Penelyn L. Acal, Helen M. Rara   +2 more
openaire   +2 more sources

Resolving sets for Johnson and Kneser graphs [PDF]

, 2012
A set of vertices $S$ in a graph $G$ is a {\em resolving set} for $G$ if, for any two vertices $u,v$, there exists $x\in S$ such that the distances $d(u,x) \neq d(v,x)$.
Alberto Márquez, Antonio González, Babai, Babai, Bailey, Bailey, Batten, Biggs, Blumenthal, Boutin, Brouwer, Cameron, Cameron, Chartrand, Chvátal, Cáceres, Cáceres, Delia Garijo, Fehr, Feng, Harary, Hughes, José Cáceres, Karen Meagher, Kaski, Kharaghani, Khuller, Kirkman, Lander, María Luz Puertas, Melter, Payne, Poisson, Robert F. Bailey, Sebő, Shanmukha, Slater, Valencia-Pabon   +37 more
core   +2 more sources