Results 11 to 20 of about 9,635,811 (355)
Graphs with equal domination and independent domination numbers [PDF]
AKCE International Journal of Graphs and Combinatorics, 2020 Let γ(G) and i(G) denote the domination number and independent domination number of a graph G. In this article, we establish a sufficient condition for a graph G to satisfy which yields some of the well known classical theorems as corollaries.
Purnima Gupta, Rajesh Singh, S. Arumugam
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Maker–Breaker Domination Number [PDF]
Bulletin of the Malaysian Mathematical Sciences Society, 2018 The Maker–Breaker domination game is played on a graph G by Dominator and Staller. The players alternatively select a vertex of G that was not yet chosen in the course of the game.
Valentin Gledel +2 more
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Bounds on the Locating-Domination Number and Differentiating-Total Domination Number in Trees
Discussiones Mathematicae Graph Theory, 2018 A subset S of vertices in a graph G = (V,E) is a dominating set of G if every vertex in V − S has a neighbor in S, and is a total dominating set if every vertex in V has a neighbor in S.
Rad Nader Jafari, Rahbani Hadi
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On the outer-independent double Italian domination number
Electronic Journal of Graph Theory and Applications, 2022 An outer-independent Italian dominating function (OIIDF) on a graph G is a function f : V ( G ) −→ { 0 , 1 , 2 } such that every vertex v ∈ V ( G ) with f ( v ) = 0 has at least two neighbors assigned 1 under f or one neighbor w with f ( w ) = 2 , and ...
Noor A'lawiah Abd Aziz +3 more
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Medium Domination Decomposition of Graphs
Ratio Mathematica, 2022 A set of vertices in a graph dominates if every vertex in is either in or adjacent to a vertex in . The size of any smallest dominating set is called domination number of .
E Ebin Raja Merly, Saranya J
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The total co-independent domination number of some graph operations
Revista de la Unión Matemática Argentina, 2022 . A set D of vertices of a graph G is a total dominating set if every vertex of G is adjacent to at least one vertex of D . The total domi- nating set D is called a total co-independent dominating set if the subgraph induced by V ( G ) − D is edgeless ...
A. Cabrera Martínez +3 more
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Further results on the total Italian domination number of trees
AIMS Mathematics, 2023 Let $ f:V(G)\rightarrow \{0, 1, 2\} $ be a function defined from a connected graph $ G $. Let $ W_i = \{x\in V(G): f(x) = i\} $ for every $ i\in \{0, 1, 2\} $. The function $ f $ is called a total Italian dominating function on $ G $ if $ \sum_{v\in N(x)}
Abel Cabrera-Martínez +2 more
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Bipartite graphs with close domination and k-domination numbers [PDF]
Open Mathematics, 2020 Abstract Let k k be a positive integer and let G
Ekinci, Gulnaz Boruzanli, Bujtas, Csilla
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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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Paired domination versus domination and packing number in graphs
Journal of Combinatorial Optimization, 2022 14 pages, 8 ...
Dettlaff, Magda +2 more
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