Results 41 to 50 of about 1,217,256 (282)

Algorithm and Hardness Results for Outer-connected Dominating Set in Graphs

Journal of Graph Algorithms and Applications, 2014
A set D ⊆ V of a graph G = (V,E) is called an outer-connected dominating set of G if for all v ∈ V, |NG[v]∩D| ≥ 1, and the induced subgraph of G on V\D is connected.
B. Panda, Arti Pandey
doaj   +1 more source

Connected power domination number of product graphs [PDF]

, 2022
In this paper, we consider the connected power domination number ($\gamma_{P, c}$) of three standard graph products. The exact value for $\gamma_{P, c}(G\circ H)$ is obtained for any two non-trivial graphs $G$ and $H.$ Further, tight upper bounds are ...
Ganesamurthy, S., Srimathi, R., Jeyaranjan, J.   +2 more
core   +1 more source

Progress on Roman and Weakly Connected Roman Graphs

Mathematics, 2021
A graph G for which γR(G)=2γ(G) is the Roman graph, and if γRwc(G)=2γwc(G), then G is the weakly connected Roman graph. In this paper, we show that the decision problem of whether a bipartite graph is Roman is a co-NP-hard problem. Next, we prove similar
Joanna Raczek, Rita Zuazua
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Connected domination critical graphs

Applied Mathematics Letters, 2004
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Xue-Gang Chen, Liang Sun, De-Xiang Ma
openaire   +1 more source

Domination Parameters of a Graph and its Complement

Discussiones Mathematicae Graph Theory, 2018
A dominating set in a graph G is a set S of vertices such that every vertex in V (G) \ S is adjacent to at least one vertex in S, and the domination number of G is the minimum cardinality of a dominating set of G.
Desormeaux Wyatt J., Haynes Teresa W., Henning Michael A.   +2 more
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Algorithmic approach, mathematical modelling and network applications of connected certified domination in graphs: A comprehensive review [PDF]

EPJ Web of Conferences
In this study we have reviewed a very important variant of graph domination theory that is connected certified domination (CCD) and also presents CCD as graph-based model for network optimization.
Nehe Reshma, Menon Radhika, Goswami Vishwajeet   +2 more
doaj   +1 more source

Triameter of Graphs

Discussiones Mathematicae Graph Theory, 2021
In this paper, we study a new distance parameter triameter of a connected graph G, which is defined as max{d(u; v)+d(v;w)+d(u;w) : u; v;w ∈ V }and is denoted by tr(G).
Das Angsuman
doaj   +1 more source

Steiner domination decomposition number of graphs

Ratio Mathematica, 2022
In this paper, we introduce a new concept Steiner domination decomposition number of graphs. Let  be a connected graph with Steiner domination numberA decomposition  of  is said to be a Steiner Domination Decomposition  if  Steiner domination ...
M Mahiba, E Ebin Raja Merly
doaj   +1 more source

Connected domination and dominating clique in trapezoid graphs

Discrete Applied Mathematics, 2000
The class of trapezoid graphs is defined as the intersection graphs of a collection of trapezoids. A set of vertices that dominates the graph and induces a connected graph is a connected dominating set. The smallest set is called the connected domination number for the graph. It is known that this problem is NP-hard.
openaire   +2 more sources

Dominating Sets and Connected Dominating Sets in Dynamic Graphs [PDF]

CoRR, 2019
In this paper we study the dynamic versions of two basic graph problems: Minimum Dominating Set and its variant Minimum Connected Dominating Set. For those two problems, we present algorithms that maintain a solution under edge insertions and edge deletions in time $O(Δ\cdot \text{polylog}~n)$ per update, where $Δ$ is the maximum vertex degree in the ...
Hjuler N., Italiano G. F., Parotsidis N., Saulpic D.   +3 more
openaire   +7 more sources