Chandrashekar Adiga, H.N. Ramaswamy, D.D. Somashekara (2004)
Discussiones Mathematicae Graph Theory
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In this note we give an upper bound for λ(n), the maximum number of edges in a strongly multiplicative graph of order n, which is sharper than the upper bound obtained by Beineke and Hegde [1].
L.W. Beineke, S.M. Hegde (2001)
Discussiones Mathematicae Graph Theory
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A graph with p vertices is said to be strongly multiplicative if its vertices can be labelled 1,2,...,p so that the values on the edges, obtained as the product of the labels of their end vertices, are all distinct. In this paper, we study structural properties of strongly multiplicative graphs. We show that all graphs in some classes, including all trees, are strongly multiplicative, and consider the question of the maximum number of edges in a strongly multiplicative graph of a given...
Terry A. McKee (2011)
Discussiones Mathematicae Graph Theory
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Define a complete subgraph Q to be simplicial in a graph G when Q is contained in exactly one maximal complete subgraph ('maxclique') of G; otherwise, Q is nonsimplicial. Several graph classes-including strong p-Helly graphs and strongly chordal graphs-are shown to have pairs of peculiarly related new characterizations: (i) for every k ≤ 2, a certain property holds for the complete subgraphs that are in k or more maxcliques of G, and (ii) in every induced subgraph H of G, that...
Anton Kundrík (1990)
Mathematica Slovaca
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C. S., Jr. Johnson, Frederick R. McMorris (1982)
Mathematica Slovaca
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Aneta Dudek, A. Paweł Wojda (2004)
Discussiones Mathematicae Graph Theory
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A graph G is said to be H-saturated if G is H-free i.e., (G has no subgraph isomorphic to H) and adding any new edge to G creates a copy of H in G. In 1986 L. Kászonyi and Zs. Tuza considered the following problem: for given m and n find the minimum size sat(n;Pₘ) of Pₘ-saturated graph of order n. They gave the number sat(n;Pₘ) for n big enough. We deal with similar problem for bipartite graphs.
Ghorbani, Ebrahim, Koolen, Jack H., Yang, Jae Young (2009)
The Electronic Journal of Combinatorics [electronic only]
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Hegde, Suresh Manjanath, Shetty, Sudhakar (2006)
Applied Mathematics E-Notes [electronic only]
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Manju K. Menon, A. Vijayakumar (2010)
Discussiones Mathematicae Graph Theory
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The edge C₄ graph of a graph G, E₄(G) is a graph whose vertices are the edges of G and two vertices in E₄(G) are adjacent if the corresponding edges in G are either incident or are opposite edges of some C₄. In this paper, we show that there exist infinitely many pairs of non isomorphic graphs whose edge C₄ graphs are isomorphic. We study the relationship between the diameter, radius and domination number of G and those of E₄(G). It is shown that for any graph G without isolated vertices,...
Lutz Volkmann (2013)
Discussiones Mathematicae Graph Theory
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Let G be a finite and simple graph with vertex set V (G), and let f V (G) → {−1, 1} be a two-valued function. If ∑x∈N|v| f(x) ≤ 1 for each v ∈ V (G), where N[v] is the closed neighborhood of v, then f is a signed 2-independence function on G. The weight of a signed 2-independence function f is w(f) =∑v∈V (G) f(v). The maximum of weights w(f), taken over all signed 2-independence functions f on G, is the signed 2-independence number α2s(G) of G. In this work, we mainly present upper bounds...
Tanenbaum, Paul J. (2000)
The Electronic Journal of Combinatorics [electronic only]
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Lucjan Szamkołowicz (1987)
Colloquium Mathematicae
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J. Nieminen (1975)
Applicationes Mathematicae
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Jenő Szigeti, Zsolt Tuza (1997)
Discussiones Mathematicae Graph Theory
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Gallai and Roy proved that a graph is k-colorable if and only if it has an orientation without directed paths of length k. We initiate the study of analogous characterizations for the existence of generalized graph colorings, where each color class induces a subgraph satisfying a given (hereditary) property. It is shown that a graph is partitionable into at most k independent sets and one induced matching if and only if it admits an orientation containing no subdigraph from a family...