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Isolate and independent domination number of some classes of graphs
AKCE International Journal of Graphs and Combinatorics, 2019 In this paper we compute isolate domination number and independent domination number of some well known classes of graphs. Also a counter example is provided, which disprove the result on independent domination for Euler Totient Cayley graph proved by ...
Shilpa T. Bhangale, Madhukar M. Pawar
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On trees with equal Roman domination and outer-independent Roman domination number [PDF]
Communications in Combinatorics and Optimization, 2019 A Roman dominating function (RDF) on a graph $G$ is a function $f : V (G) \to \{0, 1, 2\}$ satisfying the condition that every vertex $u$ for which $f(u) = 0$ is adjacent to at least one vertex $v$ for which $f(v) = 2$.
S. Nazari-Moghaddam, S.M. Sheikholeslami
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Domination and Independent Domination in Hexagonal Systems [PDF]
, 2021 A vertex subset D of G is a dominating set if every vertex in V(G)\D is adjacent to a vertex in D. A dominating set D is independent if G[D], the subgraph of G induced by D, contains no edge.
Norah Almalki, Pawaton Kaemawichanurat
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Independent Transversal Total Domination Versus Total Domination in Trees
Discussiones Mathematicae Graph Theory, 2021 A subset of vertices in a graph G is a total dominating set if every vertex in G is adjacent to at least one vertex in this subset. The total domination number of G is the minimum cardinality of any total dominating set in G and is denoted by γt(G).
Martínez Abel Cabrera +2 more
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Lower and upper bounds on independent double Roman domination in trees
Electronic Journal of Graph Theory and Applications, 2022 For a graph G = (V, E), a double Roman dominating function (DRDF) f : V → {0, 1, 2, 3} has the property that for every vertex v ∈ V with f(v)=0, either there exists a neighbor u ∈ N(v), with f(u)=3, or at least two neighbors x, y ∈ N(v) having f(x)=f(y ...
M. Kheibari +3 more
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An Improved Nordhaus–Gaddum-Type Theorem for 2-Rainbow Independent Domination Number
Mathematics, 2021 For a graph G, its k-rainbow independent domination number, written as γrik(G), is defined as the cardinality of a minimum set consisting of k vertex-disjoint independent sets V1,V2,…,Vk such that every vertex in V0=V(G)\(∪i=1kVi) has a neighbor in Vi ...
Enqiang Zhu
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Weak and Strong Reinforcement Number For a Graph [PDF]
, 2010 Introducing the weak reinforcement number which is the minimum number of added edges to reduce the weak dominating number, and giving some boundary of this new parameter and ...
DOGAN, Derya +2 more
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Independent strong domination number of indu-bala product of graphs [PDF]
, 2023 A set D⊂ V be the strong dominating set of G if every vertex in V − D is strongly dominated by at least one vertex in D. The strong domination number γst(G) of G is the minimum cardinality of a strong dominating set.
Priyadharshini M. +2 more
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Locally well-dominated and locally independent well-dominated graphs [PDF]
, 2003 In this article we present characterizations of locally well-dominated graphs and locally independent well-dominated graphs, and a sufficient condition for a graph to be k-locally independent well-dominated.
Zverovich, Vadim, Zverovich, Igor
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Double outer-independent domination number of graphs [PDF]
, 2022 Let G be a graph with no isolated vertex. A set D ⊆ V (G) is a double outer-independent dominating set of G if V (G)\D is an independent set and |N[v]∩D| ≥ 2 for every v ∈ V (G), where N[v] denotes the closed neighbourhood of v.
Martínez, Abel Cabrera
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