Selected Topics from the Theory of Graph Energy: Hypoenergetic Graph
Snježana Majstorović, Antoaneta Klobučar, Ivan Gutman (2009)
Zbornik Radova
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Snježana Majstorović, Antoaneta Klobučar, Ivan Gutman (2009)
Zbornik Radova
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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....
Gary Chartrand, Ortrud R. Oellermann, Sergio Ruiz (1986)
Mathematica Slovaca
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P K. Jha, G Slutzki (1991)
Applicationes Mathematicae
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Ivan Gutman, Bojana Borovićanin (2011)
Zbornik Radova
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Simic, Slobodan K. (1983)
Publications de l'Institut Mathématique. Nouvelle Série
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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...
Bijana Borovićanin, Ivan Gutman (2009)
Zbornik Radova
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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.
Ivan Gutman, Yeong Nan Yeh (1995)
Mathematica Slovaca
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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....
Vandenbussche, Jennifer, West, Douglas B. (2009)
The Electronic Journal of Combinatorics [electronic only]
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Adamaszek, Anna, Adamaszek, Michał (2011)
The Electronic Journal of Combinatorics [electronic only]
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