Results 41 to 50 of about 1,516 (111)
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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Journal of Mathematics, Volume 2024, Issue 1, 2024.A perfect Roman {3}‐dominating function on a graph G = (V, E) is a function f : V⟶{0, 1, 2, 3} having the property that if f(v) = 0, then ∑u∈N(v)f(u) = 3, and if f(v) = 1, then ∑u∈N(v)f(u) = 2 for any vertex v ∈ V. The weight of a perfect Roman {3}‐dominating function f is the sum ∑v∈Vf(v).
Ahlam Almulhim, Santi Spadaro
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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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Bounds on Watching and Watching Graph Products
Discussiones Mathematicae Graph Theory, 2022 A watchman’s walk for a graph G is a minimum-length closed dominating walk, and the length of such a walk is denoted (G). We introduce several lower bounds for such walks, and apply them to determine the length of watchman’s walks in several grids.
Dyer Danny, Howell Jared
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Secure Domination in Lict Graphs
, 2018 For any graph G = (V,E), lict graph η(G) of a graph G is the graph whose vertex set is the union of the set of edges and the set of cut-vertices of G in which two vertices are adjacent if and only if the corresponding edges are adjacent or the ...
Girish V. Rajasekharaiah +2 more
semanticscholar +1 more source
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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On Well-Covered Direct Products
Discussiones Mathematicae Graph Theory, 2022 A graph G is well-covered if all maximal independent sets of G have the same cardinality. In 1992 Topp and Volkmann investigated the structure of well-covered graphs that have nontrivial factorizations with respect to some of the standard graph products.
Kuenzel Kirsti, Rall Douglas F.
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On Independent Domination in Planar Cubic Graphs
Discussiones Mathematicae Graph Theory, 2019 A set S of vertices in a graph G is an independent dominating set of G if S is an independent set and every vertex not in S is adjacent to a vertex in S.
Abrishami Gholamreza +2 more
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Squares and difference sets in finite fields [PDF]
, 2013 For infinitely many primes p = 4k+1 we give a slightly improved upper bound for the maximal cardinality of a set B ⊂ Z p such that the difference set B−B contains only quadratic residues. Namely, instead of the ”trivial” bound |B| ≤ √p we prove |B √p
Bachoc, C. +2 more
core
On The Total Roman Domination in Trees
Discussiones Mathematicae Graph Theory, 2019 A total Roman dominating function on a graph G is a function f : V (G) → {0, 1, 2} satisfying the following conditions: (i) every vertex u for which f(u) = 0 is adjacent to at least one vertex v for which f(v) = 2 and (ii) the subgraph of G induced by ...
Amjadi Jafar +2 more
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