Results 41 to 50 of about 473,067 (264)
Total k-domination in strong product graphs
Discrete Applied Mathematics, 2019 Let G = ( V , E ) be a graph, a set S ⊆ V is a total k -dominating set if every vertex v ∈ V has at least k neighbors in S . The total k -domination number γ k t ( G ) is the minimum cardinality among all total k -dominating sets.
S. Bermudo +2 more
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NZ‐flows in strong products of graphs
Journal of Graph Theory, 2010 AbstractWe prove that the strong product G1⊠ G2 of G1 and G2 is ℤ3‐flow contractible if and only if G1⊠ G2 is not T⊠ K2, where T is a tree (we call T⊠ K2 a K4‐tree). It follows that G1⊠ G2 admits an NZ 3 ‐flow unless G1⊠ G2 is a K4 ‐tree. We also give a constructive proof that yields a polynomial algorithm whose output is an NZ 3‐flow if G1⊠ G2 is not ...
Wilfried Imrich +3 more
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On global (strong) defensive alliances in some product graphs
Communications in Combinatorics and Optimization, 2017 A defensive alliance in a graph is a set $S$ of vertices with the property that every vertex in $S$ has at most one more neighbor outside of $S$ than it has inside of $S$. A defensive alliance $S$ is called global if it forms a dominating set. The
Ismael Gonz\'alez Yero +2 more
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A Local Prime Factor Decomposition Algorithm for Strong Product Graphs [PDF]
Discrete Mathematics, 2011 This work is concerned with the prime factor decomposition (PFD) of strong product graphs. A new quasi-linear time algorithm for the PFD with respect to the strong product for arbitrary, finite, connected, undirected graphs is derived.
M. Hellmuth
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A Novel Study of Graphs Based on m-Polar Cubic Structures
Journal of Function Spaces, 2022 By combining the notions of interval-valued m-polar fuzzy graphs and m-polar fuzzy graphs, the notion of m-polar cubic graphs is first introduced. Then, the degree of a vertex in m-polar cubic graphs and complete m-polar cubic graphs is defined.
G. Muhiuddin +4 more
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Bounds for the pebbling number of product graphs [PDF]
Transactions on Combinatorics, 2022 Let $G$ be a connected graph. Given a configuration of a fixed number of pebbles on the vertex set of $G$, a pebbling move on $G$ is the process of removing two pebbles from a vertex and adding one pebble on an adjacent vertex. The pebbling number of $G$,
Nopparat Pleanmani +2 more
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On the strong metric dimension of product graphs
Electronic Notes in Discrete Mathematics, 2014 Abstract Let G be a connected graph. 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 of vertices of G is strongly resolved by ...
Dorota Kuziak +2 more
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Strong Total Monophonic Problems in Product Graphs, Networks, and Its Computational Complexity
Journal of Mathematics, 2022 Let G be a graph with vertex set as VG and edge set as EG which is simple as well as connected. The problem of strong total monophonic set is to find the set of vertices T⊆VG, which contains no isolated vertices, and all the vertices in VG\T lie on a ...
Eddith Sarah Varghese +5 more
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Derivable Single Valued Neutrosophic Graphs Based on KM-Fuzzy Metric
IEEE Access, 2020 In this paper we consider the concept of KM-fuzzy metric spaces and we introduce a novel concept of KM-single valued neutrosophic metric graphs based on KM-fuzzy metric spaces.
Mohammad Hamidi, Florentin Smarandache
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Local Algorithms for the Prime Factorization of Strong Product Graphs [PDF]
Mathematics and Computer Science, 2009 .The practical application of graph prime factorization algorithms is limited in practice by unavoidable noise in the data. A first step towards error-tolerant “approximate” prime factorization, is the development of local approaches that cover the graph
M. Hellmuth +3 more
semanticscholar +1 more source