The Complexity of the Super Subdivision of Cycle-Related Graphs Using Block Matrices

IF 1.9 Q2 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

Computation Pub Date : 2023-08-15 DOI:10.3390/computation11080162

Mohamed R. Zeen El Deen, Walaa A. Aboamer, H. El-Sherbiny

引用次数: 0

Abstract

The complexity (number of spanning trees) in a finite graph Γ (network) is crucial. The quantity of spanning trees is a fundamental indicator for assessing the dependability of a network. The best and most dependable network is the one with the most spanning trees. In graph theory, one constantly strives to create novel structures from existing ones. The super subdivision operation produces more complicated networks, and the matrices of these networks can be divided into block matrices. Using methods from linear algebra and the characteristics of block matrices, we derive explicit formulas for determining the complexity of the super subdivision of a certain family of graphs, including the cycle Cn, where n=3,4,5,6; the dumbbell graph Dbm,n; the dragon graph Pm(Cn); the prism graph Πn, where n=3,4; the cycle Cn with a Pn2-chord, where n=4,6; and the complete graph K4. Additionally, 3D plots that were created using our results serve as illustrations.

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循环相关图的块矩阵超细分的复杂性

Γ（网络）中的复杂性（生成树的数量）是至关重要的。生成树的数量是评估网络可靠性的基本指标。最好、最可靠的网络是具有最多生成树的网络。在图论中，人们不断地努力从现有的结构中创造出新颖的结构。超细分运算产生了更复杂的网络，这些网络的矩阵可以划分为块矩阵。利用线性代数的方法和块矩阵的特征，我们导出了确定一类图的超细分复杂度的显式公式，包括循环Cn，其中n=3，4，5，6；哑铃图Dbm，n；龙图Pm（Cn）；棱柱图πn，其中n=3，4；具有Pn2弦的周期Cn，其中n＝4,6；以及完整的图K4。此外，使用我们的结果创建的3D图也可以作为插图。

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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来源期刊

Computation Mathematics-Applied Mathematics

CiteScore

3.50

自引率

4.50%

发文量

201

审稿时长

8 weeks

期刊介绍： Computation a journal of computational science and engineering. Topics: computational biology, including, but not limited to: bioinformatics mathematical modeling, simulation and prediction of nucleic acid (DNA/RNA) and protein sequences, structure and functions mathematical modeling of pathways and genetic interactions neuroscience computation including neural modeling, brain theory and neural networks computational chemistry, including, but not limited to: new theories and methodology including their applications in molecular dynamics computation of electronic structure density functional theory designing and characterization of materials with computation method computation in engineering, including, but not limited to: new theories, methodology and the application of computational fluid dynamics (CFD) optimisation techniques and/or application of optimisation to multidisciplinary systems system identification and reduced order modelling of engineering systems parallel algorithms and high performance computing in engineering.