Computing The Energy of Certain Graphs based on Vertex Status.

IF 1.7 4区化学 Q3 CHEMISTRY, ORGANIC Current organic synthesis Pub Date : 2023-08-11 DOI:10.2174/1570179420666230811124140

Asim Khurshid, Muhammad Salman

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Abstract

Background: The concept of Hückel molecular orbital theory is used to compute the graph energy numerically as well asnd graphically, on the base of the status of a vertex.

Objective: Our aim is to explore the graph energy of various graph families on the base of the status adjacency matirx matrix and its Laplacian version.

Method: We opt for the technique of finding eigenvalues of adjacency and Laplacian matrices constructed on the base of the status of vertices.

Results: We explore the exact status sum and Laplacian status sum energies of a complete graph, complete bipartite graph, star graphs, bistar graphs, barbell graphs and graphs of two thorny rings. We also compared the obtained results of energy numerically and graphically.

Conclusion: In this article, we extended the study of graph spectrum and energy by introducing the new concept of the status sum adjacency matrix and the Laplacian status sum adjacency matrix of a graph. We investigated and visualized these newly defined spectrums and energies of well-known graphs, such as complete graphs, complete bi-graphs, star graphs, friendship graphs, bistar graphs, barbell graphs, and thorny graphs with 3 and 4 cycles.

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基于顶点状态计算某些图的能量。

背景:利用h ckel分子轨道理论的概念，以顶点的状态为基础，进行图形能量的数值计算和图形计算。目的:在状态邻接矩阵矩阵及其拉普拉斯版本的基础上，探讨各种图族的图能。方法:采用基于顶点状态构造的邻接矩阵和拉普拉斯矩阵的特征值查找技术。结果:探讨了完全图、完全二部图、星图、双星图、杠铃图和两刺环图的精确状态和能量和拉普拉斯状态和能量。并对得到的能量计算结果进行了数值和图形比较。结论:本文通过引入图的状态和邻接矩阵和拉普拉斯状态和邻接矩阵的新概念，扩展了图谱和图能量的研究。我们研究并可视化了这些新定义的已知图的谱和能量，如完全图、完全双图、星图、友谊图、双星图、杠铃图和3和4个循环的棘手图。

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来源期刊

Current organic synthesis 化学-有机化学

CiteScore

3.40

自引率

5.60%

发文量

审稿时长

6-12 weeks

期刊介绍： Current Organic Synthesis publishes in-depth reviews, original research articles and letter/short communications on all areas of synthetic organic chemistry i.e. asymmetric synthesis, organometallic chemistry, novel synthetic approaches to complex organic molecules, carbohydrates, polymers, protein chemistry, DNA chemistry, supramolecular chemistry, molecular recognition and new synthetic methods in organic chemistry. The frontier reviews provide the current state of knowledge in these fields and are written by experts who are internationally known for their eminent research contributions. The journal is essential reading to all synthetic organic chemists. Current Organic Synthesis should prove to be of great interest to synthetic chemists in academia and industry who wish to keep abreast with recent developments in key fields of organic synthesis.