Results 31 to 40 of about 5,793,190 (230)
Restrained 2-Resolving Dominating Sets in the Join, Corona and Lexicographic Product of Two Graphs
European Journal of Pure and Applied Mathematics, 2022 Let G be a connected graph. An ordered set of vertices {v1, ..., vl} is a 2-resolving set for G if, for any distinct vertices u, w ∈ V (G), the lists of distances (dG(u, v1), ..., dG(u, vl)) and (dG(w, v1), ..., dG(w, vl)) differ in at least 2 positions.
Jean Mansanadez Cabaro, Helen M. Rara
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Automorphisms of lexicographic products
Discrete Mathematics, 1975 AbstractThe automorphism group Γ(P) of a partially ordered set P consists of all permutations on P that preserve order (and have order preserving inverses). In this paper we raise, and partially answer, the question: How is the automorphism group of the lexicographic product (P × Q) of two orders (P and Q) related to the automorphism groups of the ...
Elliot Bird +2 more
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On 2-Resolving Hop Dominating Sets in the Join, Corona and Lexicographic Product of Graphs
European Journal of Pure and Applied Mathematics, 2022 Let G be a connected graph. A set S of vertices in G is a 2-resolving hop dominating set of G if S is a 2-resolving set in G and for every vertex x ∈ V (G)\S there exists y ∈ S such that dG(x, y) = 2.
A. M. Mahistrado, Helen M. Rara
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On the first and second Zagreb indices of some products of signed graphs
AKCE International Journal of Graphs and Combinatorics, 2023 Some of the most comprehensively studied degree-based topological indices are the Zagreb indices. In this article, the pair of Zagreb indices have been determined for five product graphs namely tensor product, Cartesian product, lexicographic product ...
Shivani Rai, Biswajit Deb
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On star and acyclic coloring of generalized lexicographic product of graphs
AIMS Mathematics, 2022 A $ star \; coloring $ of a graph $ G $ is a proper vertex coloring of $ G $ such that any path of length 3 in $ G $ is not bicolored. The $ star \; chromatic \; number $ $ \chi_s(G) $ of $ G $ is the smallest integer $ k $ for which $ G $ admits a star ...
Jin Cai, Shuangliang Tian, Lizhen Peng
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Total Coloring Conjecture for Certain Classes of Graphs
Algorithms, 2018 A total coloring of a graph G is an assignment of colors to the elements of the graph G such that no two adjacent or incident elements receive the same color.
R. Vignesh, J. Geetha, K. Somasundaram
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On matching extendability of lexicographic products
RAIRO - Operations Research, 2017 Summary: A graph \(G\) of even order is \(\ell\)-extendable if it is of order at least \(2\ell+2\), contains a matching of size \(\ell\), and if every such matching is contained in a perfect matching of \(G\). In this paper, we study the extendability of lexicographic products of graphs.
Nina Chiarelli +4 more
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On the indices of certain graph products [PDF]
Transactions on CombinatoricsMolecular descriptors are numerical graph invariants that are used to study the chemical structure of molecules. In this paper, we determine the upper bound of the Sombor index based on four operations involving the subdivision graph, semi-total point ...
Ishita Sarkar, Manjunath Nanjappa
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Closed formulas for the total Roman domination number of lexicographic product graphs
Ars Math. Contemp., 2021 Let G be a graph with no isolated vertex and f : V ( G ) → {0, 1, 2} a function. Let V i = { x ∈ V ( G ) : f ( x ) = i } for every i ∈ {0, 1, 2} . We say that f is a total Roman dominating function on G if every vertex in V 0 is adjacent to at least
Abel Cabrera Martínez +1 more
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Identifying Codes of Lexicographic Product of Graphs [PDF]
The Electronic Journal of Combinatorics, 2012 Let $G$ be a connected graph and $H$ be an arbitrary graph. In this paper, we study the identifying codes of the lexicographic product $G[H]$ of $G$ and $H$. We first introduce two parameters of $H$, which are closely related to identifying codes of $H$. Then we provide the sufficient and necessary condition for $G[H]$ to be identifiable.
Min Feng, Min Xu, Kaishun Wang
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