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Protection of Lexicographic Product Graphs
Discussiones Mathematicae Graph Theory, 2022 In this paper, we study the weak Roman domination number and the secure domination number of lexicographic product graphs. In particular, we show that these two parameters coincide for almost all lexicographic product graphs. Furthermore, we obtain tight
Klein Douglas J. +1 more
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Total Protection of Lexicographic Product Graphs
Discussiones Mathematicae Graph Theory, 2022 Given a graph G with vertex set V (G), a function f : V (G) → {0, 1, 2} is said to be a total dominating function if Σu∈N(v) f(u) > 0 for every v ∈ V (G), where N(v) denotes the open neighbourhood of v. Let Vi = {x ∈ V (G) : f(x) = i}. A total dominating
Martínez Abel Cabrera +1 more
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Some diameter notions in lexicographic product [PDF]
Electronic Journal of Graph Theory and Applications, 2018 Many graphs such as hypercubes, star graphs, pancake graphs, grid, torus etc are known to be good interconnection network topologies. In any network topology, the vertices represent the processors and the edges represent links between the processors. Two
Chithra MR +2 more
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Utilizing lexicographic max product of picture fuzzy graph in human trafficking
Ain Shams Engineering JournalGraph structures are an essential tool for solving combinatorial problems in computer science and computational intelligence. With an emphasis on signed graphs, picture-fuzzy graphs, and graphs with colored or labeled edges, this study explores the ...
Peide Liu +4 more
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The Spectrum of Weighted Lexicographic Product on Self-Complementary Graphs
IEEE Access, 2023 The lexicographic product, a powerful binary operation in graph theory, offers methods for creating a novel graph by establishing connections between each vertex of one graph and every vertex of another.
Xiaoxiao Zhang, Zenghui Fang
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Functorial equations for lexicographic products [PDF]
Proceedings of the American Mathematical Society, 2003 Summary: We generalize the main result of an earlier paper by the authors [Proc. Am. Math. Soc. 125, 3177-3183 (1997; Zbl 0888.12004)] concerning the convex embeddings of a chain \(\Gamma\) in a lexicographic power \(\Delta^{\Gamma}\). For a fixed non-empty chain \(\Delta\), we derive necessary and sufficient conditions for the existence of non-empty ...
Franz‐Viktor Kuhlmann +2 more
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Inverse Doubly Connected Domination in the Lexicographic Product of Two Graphs [PDF]
International Journal For Multidisciplinary ResearchLet G be a nontrivial connected graph. A dominating set D⊆V(G) is called a doubly connected dominating set of G if both 〈D〉 and 〈V(G)\D〉 are connected. Let D be a minimum connected dominating set of G. If S⊆V(G)\D is a connected dominating set of G, then
Khaty M. Cruz - +4 more
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Game chromatic number of lexicographic product graphs
AKCE International Journal of Graphs and Combinatorics, 2015 In this paper, we determine the exact values of the game chromatic number of lexicographic product of path P2 with path Pn, star K1,n and wheel Wn. Also we give an upper bound for the game chromatic number of lexicographic product of any two simple ...
R. Alagammai, V. Vijayalakshmi
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Edge-Transitive Lexicographic and Cartesian Products
Discussiones Mathematicae Graph Theory, 2016 In this note connected, edge-transitive lexicographic and Cartesian products are characterized. For the lexicographic product G ◦ H of a connected graph G that is not complete by a graph H, we show that it is edge-transitive if and only if G is edge ...
Imrich Wilfried +3 more
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Lexicographic Product and Isoperimetric Number [PDF]
ISRN Combinatorics, 2013 The isoperimetric number of a graph , denoted by , was introduced by Mohar (1987). A graph and a subset of its vertices are given, and let denote the edge boundary of , the set of edges which connects vertices in to vertices not in . The isoperimetric number of is defined as .
Ersin Aslan, Alpay Kırlangiç
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