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Displaying similar documents to “Real functions having graphs connected and dense in the plane”

A characterization of the interval function of a (finite or infinite) connected graph

Ladislav Nebeský (2001)

Czechoslovak Mathematical Journal

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By the interval function of a finite connected graph we mean the interval function in the sense of H. M. Mulder. This function is very important for studying properties of a finite connected graph which depend on the distance between vertices. The interval function of a finite connected graph was characterized by the present author. The interval function of an infinite connected graph can be defined similarly to that of a finite one. In the present paper we give a characterization of...

On the Maximum and Minimum Sizes of a Graph with Givenk-Connectivity

Yuefang Sun (2017)

Discussiones Mathematicae Graph Theory

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The concept of k-connectivity κk(G), introduced by Chartrand in 1984, is a generalization of the cut-version of the classical connectivity. For an integer k ≥ 2, the k-connectivity of a connected graph G with order n ≥ k is the smallest number of vertices whose removal from G produces a graph with at least k components or a graph with fewer than k vertices. In this paper, we get a sharp upper bound for the size of G with κk(G) = t, where 1 ≤ t ≤ n − k and k ≥ 3; moreover, the unique...

1-factors and characterization of reducible faces of plane elementary bipartite graphs

Andrej Taranenko, Aleksander Vesel (2012)

Discussiones Mathematicae Graph Theory

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As a general case of molecular graphs of benzenoid hydrocarbons, we study plane bipartite graphs with Kekulé structures (1-factors). A bipartite graph G is called elementary if G is connected and every edge belongs to a 1-factor of G. Some properties of the minimal and the maximal 1-factor of a plane elementary graph are given. A peripheral face f of a plane elementary graph is reducible, if the removal of the internal vertices and edges of the path that is the intersection...