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Displaying similar documents to “Distance Magic Cartesian Products of Graphs”

The Smallest Non-Autograph

Benjamin S. Baumer, Yijin Wei, Gary S. Bloom (2016)

Discussiones Mathematicae Graph Theory

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Suppose that G is a simple, vertex-labeled graph and that S is a multiset. Then if there exists a one-to-one mapping between the elements of S and the vertices of G, such that edges in G exist if and only if the absolute difference of the corresponding vertex labels exist in S, then G is an autograph, and S is a signature for G. While it is known that many common families of graphs are autographs, and that infinitely many graphs are not autographs, a non-autograph has never been exhibited....

Randomly H graphs

Gary Chartrand, Ortrud R. Oellermann, Sergio Ruiz (1986)

Mathematica Slovaca

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A Triple of Heavy Subgraphs Ensuring Pancyclicity of 2-Connected Graphs

Wojciech Wide (2017)

Discussiones Mathematicae Graph Theory

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A graph G on n vertices is said to be pancyclic if it contains cycles of all lengths k for k ∈ {3, . . . , n}. A vertex v ∈ V (G) is called super-heavy if the number of its neighbours in G is at least (n+1)/2. For a given graph H we say that G is H-f1-heavy if for every induced subgraph K of G isomorphic to H and every two vertices u, v ∈ V (K), dK(u, v) = 2 implies that at least one of them is super-heavy. For a family of graphs H we say that G is H-f1-heavy, if G is H-f1-heavy for...

Nullity of Graphs

Bijana Borovićanin, Ivan Gutman (2009)

Zbornik Radova

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On the p-domination number of cactus graphs

Mostafa Blidia, Mustapha Chellali, Lutz Volkmann (2005)

Discussiones Mathematicae Graph Theory

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Let p be a positive integer and G = (V,E) a graph. A subset S of V is a p-dominating set if every vertex of V-S is dominated at least p times. The minimum cardinality of a p-dominating set a of G is the p-domination number γₚ(G). It is proved for a cactus graph G that γₚ(G) ⩽ (|V| + |Lₚ(G)| + c(G))/2, for every positive integer p ⩾ 2, where Lₚ(G) is the set of vertices of G of degree at most p-1 and c(G) is the number of odd cycles in G.

Distance 2-Domination in Prisms of Graphs

Ferran Hurtado, Mercè Mora, Eduardo Rivera-Campo, Rita Zuazua (2017)

Discussiones Mathematicae Graph Theory

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A set of vertices D of a graph G is a distance 2-dominating set of G if the distance between each vertex u ∊ (V (G) − D) and D is at most two. Let γ2(G) denote the size of a smallest distance 2-dominating set of G. For any permutation π of the vertex set of G, the prism of G with respect to π is the graph πG obtained from G and a copy G′ of G by joining u ∊ V(G) with v′ ∊ V(G′) if and only if v′ = π(u). If γ2(πG) = γ2(G) for any permutation π of V(G), then G is called a universal γ2-fixer....