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.

The fundamental group of a locally finite graph with ends-a hyperfinite approach

Isaac Goldbring, Alessandro Sisto (2016)

Fundamenta Mathematicae

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The end compactification |Γ| of a locally finite graph Γis the union of the graph and its ends, endowed with a suitable topology. We show that π₁(|Γ|) embeds into a nonstandard free group with hyperfinitely many generators, i.e. an ultraproduct of finitely generated free groups, and that the embedding we construct factors through an embedding into an inverse limit of free groups. We also show how to recover the standard description of π₁(|Γ|) given by Diestel and Sprüssel (2011). Finally,...