Mieczysław Borowiecki, Danuta Michalak, Elżbieta Sidorowicz (1997)
Discussiones Mathematicae Graph Theory
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The purpose of this paper is to present some basic properties of 𝓟-dominating, 𝓟-independent, and 𝓟-irredundant sets in graphs which generalize well-known properties of dominating, independent and irredundant sets, respectively.
Igor' E. Zverovich, Olga I. Zverovich (2004)
Discussiones Mathematicae Graph Theory
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We introduce a new hereditary class of graphs, the dominant-matching graphs, and we characterize it in terms of forbidden induced subgraphs.
Mieczysław Borowiecki, Peter Mihók, Zsolt Tuza, M. Voigt (1999)
Discussiones Mathematicae Graph Theory
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We consider the problem of the existence of uniquely partitionable planar graphs. We survey some recent results and we prove the nonexistence of uniquely (𝓓₁,𝓓₁)-partitionable planar graphs with respect to the property 𝓓₁ "to be a forest".
Gabriel Semanišin (2002)
Discussiones Mathematicae Graph Theory
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A natural generalization of the fundamental graph vertex-colouring problem leads to the class of problems known as generalized or improper colourings. These problems can be very well described in the language of reducible (induced) hereditary properties of graphs. It turned out that a very useful tool for the unique determination of these properties are generating sets. In this paper we focus on the structure of specific generating sets which provide the base for the proof of The Unique...
Mieczysław Borowiecki, Anna Fiedorowicz (2006)
Discussiones Mathematicae Graph Theory
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In this paper a concept 𝓠-Ramsey Class of graphs is introduced, where 𝓠 is a class of bipartite graphs. It is a generalization of well-known concept of Ramsey Class of graphs. Some 𝓠-Ramsey Classes of graphs are presented (Theorem 1 and 2). We proved that 𝓣₂, the class of all outerplanar graphs, is not 𝓓₁-Ramsey Class (Theorem 3). This results leads us to the concept of acyclic reducible bounds for a hereditary property 𝓟 . For 𝓣₂ we found two bounds (Theorem 4). An improvement,...
Francis K. Bell, Dragos Cvetković, Peter Rowlinson, Slobodan K. Simić (1999)
Discussiones Mathematicae Graph Theory
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This paper contains a number of results in the theory of star partitions of graphs. We illustrate a variety of situations which can arise when the Reconstruction Theorem for graphs is used, considering in particular galaxy graphs - these are graphs in which every star set is independent. We discuss a recursive ordering of graphs based on the Reconstruction Theorem, and point out the significance of galaxy graphs in this connection.
Jaroslav Ivančo (2016)
Discussiones Mathematicae Graph Theory
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A graph G is called supermagic if it admits a labelling of the edges by pairwise di erent consecutive integers such that the sum of the labels of the edges incident with a vertex is independent of the particular vertex. In this paper we will introduce some constructions of supermagic labellings of some graphs generalizing double graphs. Inter alia we show that the double graphs of regular Hamiltonian graphs and some circulant graphs are supermagic.
Zlatomir Lukić (1982)
Publications de l'Institut Mathématique
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Brouwer, A.E., Spence, E. (2009)
The Electronic Journal of Combinatorics [electronic only]
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S. F. Kapoor, Linda M. Lesniak (1976)
Colloquium Mathematicae
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Juan Alberto Rodríguez-Velázquez, Erick David Rodríguez-Bazan, Alejandro Estrada-Moreno (2017)
Discussiones Mathematicae Graph Theory
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In this paper we obtain closed formulae for several parameters of generalized Sierpiński graphs S(G, t) in terms of parameters of the base graph G. In particular, we focus on the chromatic, vertex cover, clique and domination numbers.
Brandt, Stephan, Brinkmann, Gunnar, Harmuth, Thomas (1998)
The Electronic Journal of Combinatorics [electronic only]
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José D. Alvarado, Simone Dantas, Dieter Rautenbach (2017)
Discussiones Mathematicae Graph Theory
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For a graph G, let R(G) and yr2(G) denote the Roman domination number of G and the 2-rainbow domination number of G, respectively. It is known that yr2(G) ≤ R(G) ≤ 3/2yr2(G). Fujita and Furuya [Difference between 2-rainbow domination and Roman domination in graphs, Discrete Appl. Math. 161 (2013) 806-812] present some kind of characterization of the graphs G for which R(G) − yr2(G) = k for some integer k. Unfortunately, their result does not lead to an algorithm that allows to recognize...
Sylwia Cichacz, Mateusz Nikodem (2017)
Discussiones Mathematicae Graph Theory
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A distance magic labeling of a graph G = (V,E) with |V | = n is a bijection ℓ from V to the set {1, . . . , n} such that the weight w(x) = ∑y∈NG(x) ℓ(y) of every vertex x ∈ V is equal to the same element μ, called the magic constant. In this paper, we study unions of distance magic graphs as well as some properties of such graphs.
Marián Klešč, Stefan Schrötter (2011)
Discussiones Mathematicae Graph Theory
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Kulli and Muddebihal [V.R. Kulli, M.H. Muddebihal, Characterization of join graphs with crossing number zero, Far East J. Appl. Math. 5 (2001) 87-97] gave the characterization of all pairs of graphs which join product is planar graph. The crossing number cr(G) of a graph G is the minimal number of crossings over all drawings of G in the plane. There are only few results concerning crossing numbers of graphs obtained as join product of two graphs. In the paper, the exact values of crossing...
Zdzisław Skupień (2007)
Discussiones Mathematicae Graph Theory
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Grady D. Bullington, Linda L. Eroh, Steven J. Winters (2010)
Discussiones Mathematicae Graph Theory
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Explicit formulae for the γ-min and γ-max labeling values of complete bipartite graphs are given, along with γ-labelings which achieve these extremes. A recursive formula for the γ-min labeling value of any complete multipartite is also presented.