The edge-Wiener index of a graph

Dankelmann, Peter; Gutman, Iván; Mukwembi, Simon; Swart, Henda C.

doi:10.1016/j.disc.2008.09.040

Cited by 69 publications

(35 citation statements)

References 7 publications

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“…The edge-Wiener index of a graph was introduced in [21] as the Wiener index of the line graph and has been since then intensively investigated [1,3,6,12,20,27,28]. However, the concept was studied even before as the Wiener index of line graphs, see [4,17].…”

Section: Introductionmentioning

confidence: 99%

The edge-Wiener index and the edge-hyper-Wiener index of phenylenes

Pleteršek¹

2019

Discrete Applied Mathematics

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Besides the well known Wiener index, which sums up the distances between all the pairs of vertices, and the hyper-Wiener index, which includes also the squares of distances, the edge versions of both indices attracted a lot of attention in the recent years. In this paper we consider the edge-Wiener index and the edge-hyper-Wiener index of phenylenes, which represent an important class of molecular graphs. For an arbitrary phenylene, four quotient trees based on the elementary cuts are defined in a similar way as it was previously done for benzenoid systems. The computation of the edge-Wiener index of the phenylene is then reduced to the calculation of the weighted Wiener indices of the corresponding quotient trees. Furthermore, a method for computing the edgehyper-Wiener index of phenylenes is described. Finally, the application of these results gives closed formulas for the edge-Wiener index and the edge-hyper-Wiener index of linear phenylenes.

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Section: Introductionmentioning

confidence: 99%

The edge-Wiener index and the edge-hyper-Wiener index of phenylenes

Pleteršek¹

2019

Discrete Applied Mathematics

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“…(1) and (2) are recently defined graph invariants, named the edge Wiener [4,5] and the edge Szeged index [6,7], respectively. Eq.…”

Section: Introductionmentioning

confidence: 99%

Calculating the edge Wiener and edge Szeged indices of graphs

Yousefi-Azari

Khalifeh

Ashrafi

2011

Journal of Computational and Applied Mathematics

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“…While there are other notions of index in graph theory, such as for example [17][18][19][20][21], typically motivated by applications to chemistry, our present approach goes in a different direction and is aimed at answering different questions. Other applications include: molecules in chemistry and physics.…”

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confidence: 99%

Directed Graphs, von Neumann Algebras, and Index

Cho

Jørgensen

2010

Algebr Represent Theor

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In this paper, we assign index numbers to finite directed graphs. Motivated by the indices of Jones and Watatani (from operator algebra theory), we introduce and compute a new graph-theoretical index, and consider the connection with Watatani's extended Jones index. Starting with an inclusion of finite directed graphs, we show that there is a natural subgroupoid inclusion, and then a tower of von Neumann algebras. In particular, each step in the tower having the same index number, under certain normalization.

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The edge-Wiener index of a graph

Cited by 69 publications

References 7 publications

The edge-Wiener index and the edge-hyper-Wiener index of phenylenes

The edge-Wiener index and the edge-hyper-Wiener index of phenylenes

Calculating the edge Wiener and edge Szeged indices of graphs

Directed Graphs, von Neumann Algebras, and Index

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