| 何雨微,刘蒙蒙.给定参数分子图的SDD指标的上界[J].井冈山大学自然版,2025,(1):8-13 |
| 给定参数分子图的SDD指标的上界 |
| UPPER BOUND OF SYMMETRIC DIVISION DEG INDEX OF MOLECULAR GRAPHS WITH GIVEN PARAMETERS |
| 投稿时间：2024-07-11 修订日期：2024-08-21 |
| DOI：10.3969/j.issn.1674-8085.2025.01.002 |
| 中文关键词: 分子图 SDD指标 极值图 |
| 英文关键词: molecular graph SDD index extremal graph |
| 基金项目:国家自然科学基金项目(11961040) |
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| 摘要点击次数: 134 |
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| 中文摘要: |
| 研究了给定边数和悬挂点数的n阶分子图和给定直径n阶分子树的SDD指标的上界，并刻画了相应的极值图。首先根据分子图的顶点、边以及顶点的度之间的关系，构建线性方程组，然后通过解线性方程组得到图G的SDD指标的一个表达式，最终确定了给定边数和悬挂点数的n阶分子图和给定直径的n阶分子树的SDD指标的上界及其达到上界的极值图。 |
| 英文摘要: |
| In this paper, the upper bounds of SDD index among n order molecular graphs with given edge number and pendent vertices and n order molecular trees with fixed diameter are studied, and the corresponding extremal graphs are also characterized. Firstly, based on the relationship between the vertices, edges and degrees of the graph, the system of linear equations is constructed. Then, by solving the system of linear equations, an expression of the index of the graph is obtained. Finally, the upper bounds of SDD index among all molecular graphs with given edge number and pendent vertices and molecular trees with given diameter are determined, and the corresponding extremal graphs are characterized. |
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