Alali Amal S, Sözen Esra Öztürk, Abdioğlu Cihat, Ali Shakir, Eryaşar Elif
Department of Mathematical Sciences, College of Science, Princess Nourah bint Abdulrahman University, P. O. Box-84428, Riyadh-11671, Saudi Arabia.
Department of Mathematics, Sinop University, 57000, Sinop, Turkey.
Heliyon. 2024 Jul 22;10(15):e34696. doi: 10.1016/j.heliyon.2024.e34696. eCollection 2024 Aug 15.
Topological indices are numerical parameters that indicate the topology of graphs or hypergraphs. A hypergraph consists of a vertex set and an edge set , where each edge is a subset of with at least two elements. In this paper, our main aim is to introduce a general hypergraph structure for the prime ideal sum (PIS)- graph of a commutative ring. The prime ideal sum hypergraph of a ring is a hypergraph whose vertices are all non-trivial ideals of and a subset of vertices with at least two elements is a hyperedge whenever is a prime ideal of for each non-trivial ideal , in and is maximal with respect to this property. Moreover, we also compute some degree-based topological indices (first and second Zagreb indices, forgotten topological index, harmonic index, Randić index, Sombor index) for these hypergraphs. In particular, we describe some degree-based topological indices for the newly defined algebraic hypergraph based on prime ideal sum for where , for the distinct primes and .
拓扑指数是指示图或超图拓扑结构的数值参数。超图由一个顶点集和一个边集组成，其中每条边是顶点集的一个至少有两个元素的子集。在本文中，我们的主要目的是为交换环的素理想和（PIS）图引入一种通用的超图结构。环的素理想和超图是一个超图，其顶点是环的所有非平凡理想，并且当对于环中的每个非平凡理想 、 ， 是 的素理想且关于此性质是极大时，顶点的一个至少有两个元素的子集是一条超边。此外，我们还计算了这些超图的一些基于度的拓扑指数（第一和第二 Zagreb 指数、遗忘拓扑指数、调和指数、Randić指数、Sombor 指数）。特别地，我们描述了基于素理想和为 （其中 ， 为不同的素数 、 ）新定义的代数超图的一些基于度的拓扑指数。
