Results 31 to 40 of about 477 (116)
Some Progress on the Double Roman Domination in Graphs
Discussiones Mathematicae Graph Theory, 2019 For a graph G = (V,E), a double Roman dominating function (or just DRDF) is a function f : V → {0, 1, 2, 3} having the property that if f(v) = 0 for a vertex v, then v has at least two neighbors assigned 2 under f or one neighbor assigned 3 under f, and ...
Rad Nader Jafari, Rahbani Hadi
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On the general position number of two classes of graphs
Open Mathematics, 2022 The general position problem is to find the cardinality of the largest vertex subset SS such that no triple of vertices of SS lies on a common geodesic.
Yao Yan, He Mengya, Ji Shengjin
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Connected 𝐷 - Eccentric Domination in Graphs
Indian Journal of Science and TechnologyObjectives: To introduce connected -eccentric point set, connected -eccentric number, connected -eccentric dominating set, connected -eccentric domination number in a graph and related concepts. Methods: -distance in graphs are used to find the connected
A. Prasanna, N. Mohamedazarudeen
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Double domination in maximal outerplanar graphs
Open Mathematics, 2022 In graph GG, a vertex dominates itself and its neighbors. A subset S⊆V(G)S\subseteq V\left(G) is said to be a double-dominating set of GG if SS dominates every vertex of GG at least twice.
Zhuang Wei, Zheng Qiuju
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Secure domination in the joins of graphs
, 2014 In this paper, we revisited the concept of secure dominating set introduced by Cockayne et al. We characterized secure dominating set in terms of the concept of external private neighborhood of a vertex.
Elmer C. Castillano +2 more
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On Incidence Coloring of Complete Multipartite and Semicubic Bipartite Graphs
Discussiones Mathematicae Graph Theory, 2018 In the paper, we show that the incidence chromatic number χi of a complete k-partite graph is at most Δ + 2 (i.e., proving the incidence coloring conjecture for these graphs) and it is equal to Δ + 1 if and only if the smallest part has only one vertex ...
Janczewski Robert +2 more
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On Grundy Total Domination Number in Product Graphs
Discussiones Mathematicae Graph Theory, 2021 A longest sequence (v1, . . ., vk) of vertices of a graph G is a Grundy total dominating sequence of G if for all i, N(υj)\∪j=1i-1N(υj)≠∅N({\upsilon _j})\backslash \bigcup\nolimits_{j = 1}^{i - 1} {N({\upsilon _j})} \ne \emptyset .
Brešar Boštjan +8 more
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Some Results on the Independence Polynomial of Unicyclic Graphs
Discussiones Mathematicae Graph Theory, 2018 Let G be a simple graph on n vertices. An independent set in a graph is a set of pairwise non-adjacent vertices. The independence polynomial of G is the polynomial I(G,x)=∑k=0ns(G,k)xk$I(G,x) = \sum\nolimits_{k = 0}^n {s\left({G,k} \right)x^k }$, where s(
Oboudi Mohammad Reza
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Open Locating-Dominating Sets in Circulant Graphs
Discussiones Mathematicae Graph Theory, 2022 Location detection problems have been studied for a variety of applications including finding faults in multiprocessors, contaminants in public utilities, intruders in buildings and facilities, and for environmental monitoring using wireless sensor ...
Givens Robin M. +2 more
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(Independent) $k$-Rainbow Domination of a Graph
Turkish journal of mathematics & computer science, 2020 Let G = (V, E) be a graph with the vertex set V = V(G) and the edge set E = E(G). Let k be a positive integer and γrk(G) (γirk (G)) be k-rainbow domination (independent k-rainbow domination) number of a graph G.
D. Mojdeh, Zhila Mansouri
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