Double and Strong Double of Graphs and Their Topological Indices

Subject Areas : Statistics

مهدیه آذری ¹ , فرزانه فلاحتی نژاد ²

1 - گروه ریاضی، دانشکده علوم پایه، واحد کازرون، دانشگاه آزاد اسلامی، کازرون، ایران
2 - گروه ریاضی، واحد صفادشت، دانشگاه آزاد اسلامی، تهران، ایران

Received: 2022-08-21 Accepted : 2023-02-05 Published : 2024-09-25

Keywords: گراف‌های مرکب, شاخص توپولوژیک, فاصله‌ی در گراف,

Abstract :

Let G be a simple connected graph with the vertex set V(G)={v_1,v_2,…,v_n }. The double graph of G is made from two distinct copies X={x_1,x_2,…,x_n } and Y={y_1,y_2,…,y_n } of G by adding the edges x_i y_j and x_j y_i for every edge v_i v_j of G and the strong double graph of G is obtained from the copies X and Y by joining (with an edge) the vertex x_i with the vertex y_i and the vertices adjacent with y_i for all 1≤i≤n. A topological index of G is a real number TI(G) with the property that for every graph H isomorphic to G, TI(H)=TI(G). Topological indices are considered as useful tools in predicting physico-chemical, biological, and pharmaceutical properties of chemical compounds and used in the development of quantitative structure-activity and quantitative structure-property relationships. In this paper, we study some distance-based topological indices such as the first and second status connectivity coindices, eccentric version of geometric-arithmetic index, eccentric version of atom-bond connectivity index, Szeged index, revised Szeged index, and weighted Szeged index of double graphs and strong double graphs.

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