Maximizing the Mostar index for bipartite graphs and split graphs

Miklavič, Štefko; Pardey, Johannes; Rautenbach, Dieter; Werner, Florian

doi:10.1016/j.disopt.2023.100768

Search citation statements

Order By: Relevance

Paper Sections

Select...

Introduction2

Citation Types

Supporting

Mentioning

Contrasting

Year Published

2023

2024

Publication Types

Select...

Article3

Relationship

Self Cite0

Independent3

Authors

Journals

Cited by 3 publications

(2 citation statements)

References 13 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The proof of Theorem 1 is surprisingly simple and elegant. It is based on a linear programming approach, which we developed in connection with the Mostar index [10,11], a parameter that is closely related to the irregularity [3,5,6]. Both parameters display a similar tradeoff: In order to obtain a large value of the parameter, one needs many edges, but, if there are too many edges, then the average contribution per edge goes down.…”

Section: Introductionmentioning

confidence: 99%

Irregularity of Graphs Respecting Degree Bounds

Rautenbach,

Werner

2023

Electron. J. Combin.

View full text Add to dashboard Cite

show abstract

Section: Introductionmentioning

confidence: 99%

Irregularity of Graphs Respecting Degree Bounds

Rautenbach,

Werner

2023

Electron. J. Combin.

View full text Add to dashboard Cite

show abstract

“…u). Many researchers have been extensively worked on different distance based indices, see [1,6,11,16,17,36] [13,14,23,25].…”

Section: Introductionmentioning

confidence: 99%

On Weighted Vertex and Edge Mostar Index for Trees and Cacti with Fixed Parameter

Asmat,

Askar

et al. 2023

Eur. J. Pure Appl. Math.

View full text Add to dashboard Cite

It was introduced by Doˇsli ́c and Ivica et al. (Journal of Mathematical chemistry, 56(10) (2018): 2995–3013), as an innovative graph-theoretic topological identifier, the Mostar index is significant in simulating compounds’ thermodynamic properties in simulations, which is defined as sum of absolute values of the differences among nu(e|Ω) and nv(e|Ω) over all lines e = uv ∈ Ω, where nu(e|Ω) (resp. nv(e|Ω)) is the collection of vertices of Ω closer to vertex u (resp. v) than to vertex v (resp. u). Let C(n, k) be the set of all n-vertex cacti graphs with exactly k cycles and T(n, d) be the set of all n-vertex tree graphs with diameter d. It is said that a cacti is a connected graph with blocks that comprise of either cycles or edges. Beginning with the weighted Mostar index of graphs, we developed certain transformations that either increase or decrease index. To advance this analysis, we determine the extreme graphs where the maximum and minimum values of the weighted edge Mostar index are accomplished. Moreover, we compute the maximum weighted vertex Mostar invariant for trees with order n and fixed diameter d.

show abstract