The (revised) Szeged index and the Wiener index of a nonbipartite graph

Chen, Lily; Li, Xueliang; Liu, Mengmeng

doi:10.1016/j.ejc.2013.07.019

Cited by 28 publications

(18 citation statements)

References 12 publications

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“…Theorem 1.2 (Chen et al (2014)). Let G be a connected graph with n 5 vertices with an odd cycle and girth g 5.…”

Section: Introductionmentioning

confidence: 95%

“…The equality holds if and only if G is composed of a cycle C 5 on 5 vertices, and one tree rooted at a vertex of the C 5 or two trees, respectively, rooted at two adjacent vertices of the C 5 . Theorem 1.3 (Chen et al (2014)). Let G be a connected graph with n 4 vertices and |E G | n edges and with an odd cycle.…”

Section: Introductionmentioning

confidence: 95%

“…Theorem 1.1 (Chen et al (2012(Chen et al ( , 2014). Let G be a connected bipartite graph with n 4 vertices and |E G | n edges.…”

Section: Introductionmentioning

confidence: 99%

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On the further relation between the (revised) Szeged index and the Wiener index of graphs

Zhang

Zhao

2016

Discrete Applied Mathematics

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Let Sz(G), Sz * (G) and W (G) be the Szeged index, revised Szeged index and Wiener index of a graph G. In this paper, the graphs with the fourth, fifth, sixth and seventh largest Wiener indices among all unicyclic graphs of order n 10 are characterized; and the graphs with the first, second, third, and fourth largest Wiener indices among all bicyclic graphs are identified. Based on these results, further relation on the quotients between the (revised) Szeged index and the Wiener index are studied. Sharp lower bound on Sz(G)/W (G) is determined for all connected graphs each of which contains at least one non-complete block. In addition the connected graph with the second smallest value on Sz * (G)/W (G) is identified for G containing at least one cycle.

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“…Theorem 1.2 (Chen et al (2014)). Let G be a connected graph with n 5 vertices with an odd cycle and girth g 5.…”

Section: Introductionmentioning

confidence: 95%

Section: Introductionmentioning

confidence: 95%

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On the further relation between the (revised) Szeged index and the Wiener index of graphs

Zhang

Zhao

2016

Discrete Applied Mathematics

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“…This topological index has been stuided extensively and has been found applications in modelling physicochemical properties. The upper and lower bounds and other aspects of the Wiener index of many graphs have been fully studied; see, e.g., [1,5,6,8,9,13,19,20,23].…”

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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“…Analogously Xing and Zhou [4] determined the n-vertex unicyclic graphs with the smallest, the second-smallest and the third-smallest revised Szeged index. Chen et al [5] studied the differences between the revised Szeged index and the Wiener index. Dong et al [6] considered the revised edge Szeged index of molecular graphs.…”

Section: Introductionmentioning

confidence: 99%

Revised Szeged Index and Revised Edge Szeged Index of Certain Special Molecular Graphs

Gao¹,

Gao²,

Liang³

2014

IJAPM

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Abstract:In theoretical chemistry, the revised Szeged index and revised Szeged edge index were introduced to measure the stability of alkanes and the strain energy of cycloalkanes. In this paper, by virtue of mathematical derivation, we determine the revised Szeged index and revised edge Szeged index of fan molecular graph, wheel molecular graph, gear fan molecular graph, gear wheel molecular graph, and their r-corona molecular graphs. These molecular structures are widely used in biology, medical science and pharmaceutical fields. At last, the normalized revised Szeged indexes of fan molecular graph, wheel molecular graph, gear fan molecular graph, gear wheel molecular graph, and their r-corona molecular graphs are given.

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The (revised) Szeged index and the Wiener index of a nonbipartite graph

Cited by 28 publications

References 12 publications

On the further relation between the (revised) Szeged index and the Wiener index of graphs

On the further relation between the (revised) Szeged index and the Wiener index of graphs

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

Revised Szeged Index and Revised Edge Szeged Index of Certain Special Molecular Graphs

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