Results 1 to 10 of about 26,105 (190)
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
doaj +3 more sources
Infinite Lexicographic Products [PDF]
Annals of Pure and Applied Logic, 2019 We generalize the lexicographic product of first-order structures by presenting a framework for constructions which, in a sense, mimic iterating the lexicographic product infinitely and not necessarily countably many times.
Meir, Nadav
core +2 more sources
Nonrepetitive colorings of lexicographic product of graphs [PDF]
Discrete Mathematics & Theoretical Computer Science, 2014 Special issue PRIMA ...
Balázs Keszegh +2 more
doaj +7 more sources
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
doaj +3 more sources
Pseudo MV-algebras and Lexicographic Product [PDF]
Fuzzy Sets and Systems, 2014 We study algebraic conditions when a pseudo MV-algebra is an interval in the lexicographic product of an Abelian unital $\ell$-group and an $\ell$-group that is not necessary Abelian.
Dvurečenskij, Anatolij
core +3 more sources
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
doaj +4 more sources
Lexicographic product graphs are antimagic
AKCE International Journal of Graphs and Combinatorics, 2018 A graph with edges is called if its edges can be labeled with 1, 2, , such that the sums of the labels on the edges incident to each vertex are distinct. Hartsfield and Ringel conjectured that every connected graph other than is antimagic. In this paper,
Wenhui Ma +3 more
doaj +3 more sources
Non-1-Planarity of Lexicographic Products of Graphs
Discussiones Mathematicae Graph Theory, 2021 In this paper, we show the non-1-planarity of the lexicographic product of a theta graph and K2. This result completes the proof of the conjecture that a graph G ◦ K2 is 1-planar if and only if G has no edge belonging to two cycles.
Matsumoto Naoki, Suzuki Yusuke
doaj +2 more sources
Some diameter notions in lexicographic product
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
doaj +2 more sources
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
doaj +1 more source