Results 101 to 110 of about 1,343 (197)
b -continuity and the lexicographic product of graphs
Electronic Notes in Discrete Mathematics, 2015 Abstract A k-coloring c of a graph G = ( V , E ) is a b-coloring if for every color class c i , 1 ≤ i ≤ k , there is a vertex colored i whose neighborhood intersects every other color class c j of c.
Cláudia Linhares Sales +2 more
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Countable compactness of lexicographic products of GO-spaces [PDF]
, 2019 summary:We characterize the countable compactness of lexicographic products of GO-spaces. Applying this characterization about lexicographic products, we see: \begin{itemize} \item[$\circ$] the lexicographic product $X^2$ of a countably compact GO-space $
Kemoto, Nobuyuki
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Closed Formulae for the Strong Metric Dimension of Lexicographic Product Graphs
Discussiones Mathematicae Graph Theory, 2016 Given a connected graph G, a vertex w ∈ V (G) strongly resolves two vertices u, v ∈ V (G) if there exists some shortest u − w path containing v or some shortest v − w path containing u. A set S of vertices is a strong metric generator for G if every pair
Kuziak Dorota +2 more
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Efficient domination and bondage numbers in lexicographic product of trees
MANAS: Journal of EngineeringThe vertex subset 𝑆 in 𝐺 is called the efficient dominating set, if every vertex not in 𝑆 is adjacent exactly one vertex in 𝑆 and it is also required that none of the vertices in 𝑆 are adjacent to each other. The efficient domination number 𝛾𝑒(𝐺) of 𝐺 is
Betül Atay
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QUANTUM AUTOMORPHISM GROUP OF THE LEXICOGRAPHIC PRODUCT OF FINITE REGULAR GRAPHS [PDF]
, 2015 We study the quantum automorphism group of the lexicographic product of two finite regular graphs, providing a quantum generalization of Sabidussi's structure theorem on the automorphism group of such a ...
Chassaniol, Arthur
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On alpha labeling of tensor product of paths and cycles. [PDF]
Heliyon, 2023 L U, G R.
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Geodesic dominated coloring in certain product graphs
Frontiers in Applied Mathematics and StatisticsA geodesic dominated coloring of a graph G is a proper coloring in which each color class is dominated by at least one geodesic. The minimum number of colors required for such a coloring is the geodesic dominated chromatic number, denoted by χdomg(G). In
M. Paruvatha Vathana, R. Jayagopal
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The copnumber for lexicographic products and sums of graphs
Contributions to Discrete Mathematics, 2015 For the lexicographic product G∙H of two graphs G and H so that G is connected, we prove that if the copnumber c(G) of G is greater than or equal to 2, then c(G∙H)=c(G). Moreover, if c(G)=c(H)=1, then c(G∙H)=1. If c(G)=1, G has more than one vertex, and c(H)≥2, then c(G∙H)=2. We also provide the copnumber for general lexicographic sums.
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Hamiltonian properties in generalized lexicographic products [PDF]
The lexicographic product $G[H]$ of two graphs $G$ and $H$ is obtained from $G$ by replacing each vertex with a copy of $H$ and adding all edges between any pair of copies corresponding to adjacent vertices of $G$.
Jan Ekstein +3 more
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