Cactus graphs with minimum edge revised Szeged index

Liu, Mengmeng; Wang, Shujing

doi:10.1016/j.dam.2018.03.037

Cited by 4 publications

(1 citation statement)

References 11 publications

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“…See [3,6,11,18,22] for various properties of the Szeged index of a graph. Some invariants such as edge Szeged index, revised Szeged index were also studied, see, e.g., [1,7,8,12,17,20,21]. Very recently, Doslić et al [4] introduced a new invariant -the Mostar index, of a connected graph G, defined as…”

Section: Introductionmentioning

confidence: 99%

On cacti with large Mostar index

Hayat

Zhou

2019

Filomat

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The Mostar index of a graph G is defined as the sum of absolute values of the differences between n u and n v over all edges e = uv of G, where n u (e) and n v (e) are respectively, the number of vertices of G lying closer to vertex u than to vertex v and the number of vertices of G lying closer to vertex v than to vertex u. A cactus is a graph in which any two cycles have at most one common vertex. In this paper, we determine all the n-vertex cacti with the largest Mostar index, and we give a sharp upper bound of the Mostar index for cacti of order n with k cycles, and characterize all the cacti that achieve this bound.

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Section: Introductionmentioning

confidence: 99%

On cacti with large Mostar index

Hayat

Zhou

2019

Filomat

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Maximum Balaban index and sum-Balaban index of cacti

Zuo

Yiping

et al. 2019

Discrete Math. Algorithm. Appl.

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The Balaban index and the sum-Balaban index of a graph [Formula: see text] are defined as [Formula: see text] and [Formula: see text], respectively, where [Formula: see text] is the distance sum of vertex [Formula: see text] in [Formula: see text], [Formula: see text] is the number of edges and [Formula: see text] is the cyclomatic number of [Formula: see text]. A connected graph [Formula: see text] is said to be a cactus if each of its blocks is either a cycle or an edge. In this paper, we determine the maximum values of Balaban index and sum-Balaban index and characterize the corresponding extremal graphs among all cacti with [Formula: see text] vertices and [Formula: see text] cycles.

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Comparison between Szeged indices of graphs

Das

Ашрафи

2019

Quaestiones Mathematicae

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Cactus graphs with minimum edge revised Szeged index

Cited by 4 publications

References 11 publications

On cacti with large Mostar index

On cacti with large Mostar index

Maximum Balaban index and sum-Balaban index of cacti

Comparison between Szeged indices of graphs

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