Bounds for the Sum-Balaban index and (revised) Szeged index of regular graphs

Lei, Hui; Hua, Yuan‐Zhao

doi:10.1016/j.amc.2015.07.021

Cited by 9 publications

(7 citation statements)

References 15 publications

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“…We also consider a similar result for the Wiener index, which was proved in [20] under the name partition distance. In Section 4 we show that 25 the mentioned results generalize already known results for benzenoid systems (see [4,6]) and apply them to C 4 C 8 systems. Furthermore, we demonstrate with an example that the method can also be used to calculate the corresponding indices by hand.…”

Section: Introductionsupporting

confidence: 66%

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The Szeged index and the Wiener index of partial cubes with applications to chemical graphs

repnjak

Tratnik

2017

Applied Mathematics and Computation

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In this paper we study the Szeged index of partial cubes and hence generalize the result proved by V. Chepoi and S. Klavžar, who calculated this index for benzenoid systems. It is proved that the problem of calculating the Szeged index of a partial cube can be reduced to the problem of calculating the Szeged indices of weighted quotient graphs with respect to a partition coarser than Θ-partition. Similar result for the Wiener index was recently proved by S. Klavžar and M. J. Nadjafi-Arani. Furthermore, we show that such quotient graphs of partial cubes are again partial cubes. Since the results can be used to efficiently calculate the Wiener index and the Szeged index for specific families of chemical graphs, we consider C 4 C 8 systems and show that the two indices of these graphs can be computed in linear time.

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Section: Introductionsupporting

confidence: 66%

“…This topological index was later named as the Szeged index. For some recent results on the Wiener index and the Szeged index see [1,11,22,23,25,28]. Moreover, some other variants of the Wiener index were 15 introduced, for example Wiener polarity index (see [10,24,26]).…”

Section: Introductionmentioning

confidence: 99%

The Szeged index and the Wiener index of partial cubes with applications to chemical graphs

repnjak

Tratnik

2017

Applied Mathematics and Computation

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“…In [21] we found an erroneous statement that complete graphs attain the maximum sum-Balaban index among all n-vertex graphs. However this is true only for small cases of n as proved in [20].…”

Section: Maximum Valuesmentioning

confidence: 92%

Sum-Balaban index and its properties

Knor¹,

Škrekovski²,

Tepeh³

2017

Proceedings of the 1st Croatian Combinatorial Days

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The sum-Balaban index is defined as SJ(G) = m m−n+2 1 √ w(u)+w(v) , where the sum is taken over all edges of a connected graph G, n and m are the cardinalities of the vertex and the edge set of G, respectively, and w(u) (resp. w(v)) denotes the sum of distances from u (resp. v) to all the other vertices of G. In the paper known results on this recently introduced topological index are summarized.

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“…Since it has been proved to be of great applications in the study of the modeling physicochemical properties of chemical compounds and drugs, the Szeged index has been studied extensively by many researchers, see, e.g., [2,3,5,7,14,15,16,18,21,22,24].…”

Section: Introductionmentioning

confidence: 99%

On extremal cacti with respect to the edge Szeged index and edge-vertex Szeged index

He¹,

Hao²,

Yu³

2018

Filomat

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The edge Szeged index and edge-vertex Szeged index of a graph are defined as Sz e (G) =respectively, where m u (uv|G) (resp., m v (uv|G)) is the number of edges whose distance to vertex u (resp., v) is smaller than the distance to vertex v (resp., u), and n u (uv|G) (resp., n v (uv|G)) is the number of vertices whose distance to vertex u (resp., v) is smaller than the distance to vertex v (resp., u), respectively. A cactus is a graph in which any two cycles have at most one common vertex. In this paper, the lower bounds of edge Szeged index and edge-vertex Szeged index for cacti with order n and k cycles are determined, and all the graphs that achieve the lower bounds are identified.

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Bounds for the Sum-Balaban index and (revised) Szeged index of regular graphs

Cited by 9 publications

References 15 publications

The Szeged index and the Wiener index of partial cubes with applications to chemical graphs

The Szeged index and the Wiener index of partial cubes with applications to chemical graphs

Sum-Balaban index and its properties

On extremal cacti with respect to the edge Szeged index and edge-vertex Szeged index

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