Displaying similar documents to “A Note on Total Graphs”

The periphery graph of a median graph

Boštjan Brešar, Manoj Changat, Ajitha R. Subhamathi, Aleksandra Tepeh (2010)

Discussiones Mathematicae Graph Theory

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The periphery graph of a median graph is the intersection graph of its peripheral subgraphs. We show that every graph without a universal vertex can be realized as the periphery graph of a median graph. We characterize those median graphs whose periphery graph is the join of two graphs and show that they are precisely Cartesian products of median graphs. Path-like median graphs are introduced as the graphs whose periphery graph has independence number 2, and it is proved that there are...

The Existence Of P≥3-Factor Covered Graphs

Sizhong Zhou, Jiancheng Wu, Tao Zhang (2017)

Discussiones Mathematicae Graph Theory

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A spanning subgraph F of a graph G is called a P≥3-factor of G if every component of F is a path of order at least 3. A graph G is called a P≥3-factor covered graph if G has a P≥3-factor including e for any e ∈ E(G). In this paper, we obtain three sufficient conditions for graphs to be P≥3-factor covered graphs. Furthermore, it is shown that the results are sharp.

α-Labelings of a Class of Generalized Petersen Graphs

Anna Benini, Anita Pasotti (2015)

Discussiones Mathematicae Graph Theory

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An α-labeling of a bipartite graph Γ of size e is an injective function f : V (Γ) → {0, 1, 2, . . . , e} such that {|ƒ(x) − ƒ(y)| : [x, y] ∈ E(Γ)} = {1, 2, . . . , e} and with the property that its maximum value on one of the two bipartite sets does not reach its minimum on the other one. We prove that the generalized Petersen graph PSn,3 admits an α-labeling for any integer n ≥ 1 confirming that the conjecture posed by Vietri in [10] is true. In such a way we obtain an infinite class...

Pₘ-saturated bipartite graphs with minimum size

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.

On universal graphs for hom-properties

Peter Mihók, Jozef Miškuf, Gabriel Semanišin (2009)

Discussiones Mathematicae Graph Theory

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A graph property is any isomorphism closed class of simple graphs. For a simple finite graph H, let → H denote the class of all simple countable graphs that admit homomorphisms to H, such classes of graphs are called hom-properties. Given a graph property 𝓟, a graph G ∈ 𝓟 is universal in 𝓟 if each member of 𝓟 is isomorphic to an induced subgraph of G. In particular, we consider universal graphs in → H and we give a new proof of the existence of a universal graph in → H, for any finite...

Regularity and Planarity of Token Graphs

Walter Carballosa, Ruy Fabila-Monroy, Jesús Leaños, Luis Manuel Rivera (2017)

Discussiones Mathematicae Graph Theory

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Let G = (V, E) be a graph of order n and let 1 ≤ k < n be an integer. The k-token graph of G is the graph whose vertices are all the k-subsets of V, two of which are adjacent whenever their symmetric difference is a pair of adjacent vertices in G. In this paper we characterize precisely, for each value of k, which graphs have a regular k-token graph and which connected graphs have a planar k-token graph.

On H-Irregularity Strength Of Graphs

Faraha Ashraf, Martin Bača, Marcela Lascśaková, Andrea Semaničová-Feňovčíková (2017)

Discussiones Mathematicae Graph Theory

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New graph characteristic, the total H-irregularity strength of a graph, is introduced. Estimations on this parameter are obtained and for some families of graphs the precise values of this parameter are proved.