Displaying similar documents to “p-Wiener intervals and p-Wiener free intervals”

The Steiner Wiener Index of A Graph

Xueliang Li, Yaping Mao, Ivan Gutman (2016)

Discussiones Mathematicae Graph Theory

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The Wiener index W(G) of a connected graph G, introduced by Wiener in 1947, is defined as W(G) = ∑u,v∈V(G) d(u, v) where dG(u, v) is the distance between vertices u and v of G. The Steiner distance in a graph, introduced by Chartrand et al. in 1989, is a natural generalization of the concept of classical graph distance. For a connected graph G of order at least 2 and S ⊆ V (G), the Steiner distance d(S) of the vertices of S is the minimum size of a connected subgraph whose vertex set...

Wiener index of generalized stars and their quadratic line graphs

Andrey A. Dobrynin, Leonid S. Mel'nikov (2006)

Discussiones Mathematicae Graph Theory

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The Wiener index, W, is the sum of distances between all pairs of vertices in a graph G. The quadratic line graph is defined as L(L(G)), where L(G) is the line graph of G. A generalized star S is a tree consisting of Δ ≥ 3 paths with the unique common endvertex. A relation between the Wiener index of S and of its quadratic graph is presented. It is shown that generalized stars having the property W(S) = W(L(L(S)) exist only for 4 ≤ Δ ≤ 6. Infinite families of generalized stars with this...

A Note on the Interval Function of a Disconnected Graph

Manoj Changat, Ferdoos Hossein Nezhad, Henry Martyn Mulder, N. Narayanan (2018)

Discussiones Mathematicae Graph Theory

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In this note we extend the Mulder-Nebeský characterization of the interval function of a connected graph to the disconnected case. One axiom needs to be adapted, but also a new axiom is needed in addition.

The Wiener number of Kneser graphs

Rangaswami Balakrishnan, S. Francis Raj (2008)

Discussiones Mathematicae Graph Theory

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The Wiener number of a graph G is defined as 1/2∑d(u,v), where u,v ∈ V(G), and d is the distance function on G. The Wiener number has important applications in chemistry. We determine the Wiener number of an important family of graphs, namely, the Kneser graphs.

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 number of representations of an element in a polygonal Cayley graph

Gabriella Kuhn, Paolo M. Soardi (1987)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

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We compute explicitly the number of paths of given length joining two vertices of the Cayley graph of the free product of cyclic groups of order k.