Noureen Sadia, Batool Rimsha, Albalahi Abeer M, Shang Yilun, Alraqad Tariq, Ali Akbar
Department of Mathematics, Faculty of Science, University of Gujrat, Gujrat, Pakistan.
Department of Mathematics, College of Science, University of Ha'il, Ha'il, Saudi Arabia.
Heliyon. 2024 Jul 3;10(14):e33841. doi: 10.1016/j.heliyon.2024.e33841. eCollection 2024 Jul 30.
The sum-connectivity, Randić, and atom-bond connectivity indices have a prominent place among those topological indices that depend on the graph's vertex degrees. The ABS (atom-bond sum-connectivity) index is a variant of all the aforementioned three indices, which was recently put forward. Let be the class of all connected tricyclic graphs of order . Recently, the problem of determining graphs from having the least possible value of the ABS index was solved in (Zuo et al., 2024 [39]) for the case when the maximum degree of the considered graphs does not exceed 4. The present paper addresses the problem of finding graphs from having the largest possible value of the ABS index for .
在那些依赖于图的顶点度的拓扑指数中，和连通性、兰迪奇指数以及原子键连通性指数占据着显著地位。ABS（原子键和连通性）指数是上述三个指数的一种变体，它是最近才被提出的。设 为所有阶数为 的连通三圈图的类。最近，在（左等人，2024 [39]）中解决了确定 类中具有最小ABS指数值的图的问题，该问题针对所考虑的图的最大度不超过4的情况。本文解决了对于 ，在 类中找到具有最大可能ABS指数值的图的问题。
