最小化具有固定大小和直径的二方图中的第二个萨格勒布偏心指数

IF 2.4 3区数学 Q1 MATHEMATICS Journal of Applied Mathematics and Computing Pub Date : 2024-06-29 DOI:10.1007/s12190-024-02163-8

Fazal Hayat, Shou-Jun Xu, Xuli Qi

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引用次数: 0

摘要

对于给定的图 G，第二萨格勒布偏心指数（\xi _2 (G)\）被定义为 G 中两个相邻顶点对的偏心率的乘积。本文主要研究在具有固定边数和直径的 n 个顶点双artite图中确定最小化第二萨格勒布偏心指数的图的问题。具体地说，我们确定了在固定边数和直径的 n 阶双方形中第二萨格勒布偏心指数的尖锐下限。达到这些下界的极值图被完全表征出来。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Minimizing the second Zagreb eccentricity index in bipartite graphs with a fixed size and diameter

For a given graph G, the second Zagreb eccentricity index \(\xi _2 (G)\) is defined as the product of the eccentricities of two adjacent vertex pairs in G. This paper mainly studies the problem of determining the graphs that minimize the second Zagreb eccentricity index among n-vertex bipartite graphs with a fixed number of edges and diameter. To be specific, we determine the sharp lower bound on the second Zagreb eccentricity index over the bipartite graphs of order n in terms of fixed edges and diameter. The extremal graphs attaining these lower bounds are fully characterized.

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来源期刊

Journal of Applied Mathematics and Computing Mathematics-Computational Mathematics

CiteScore

4.20

自引率

4.50%

发文量

131

期刊介绍： JAMC is a broad based journal covering all branches of computational or applied mathematics with special encouragement to researchers in theoretical computer science and mathematical computing. Major areas, such as numerical analysis, discrete optimization, linear and nonlinear programming, theory of computation, control theory, theory of algorithms, computational logic, applied combinatorics, coding theory, cryptograhics, fuzzy theory with applications, differential equations with applications are all included. A large variety of scientific problems also necessarily involve Algebra, Analysis, Geometry, Probability and Statistics and so on. The journal welcomes research papers in all branches of mathematics which have some bearing on the application to scientific problems, including papers in the areas of Actuarial Science, Mathematical Biology, Mathematical Economics and Finance.