Further Results on Wiener Polarity Index of Graphs

شاخص وينر قطبي يك گراف ملكولي از مرتبه عبارتh ست از تعداد زوج هاي نامرتب از ريوس و از به طوري كه . قبلا در برخي خواص فرين اين پاياي گراف در مورد گراف هاي فولرين و سيستم هاي شش ضلعي كاتاچگال مورد بررسي قرار گرفته است. در اين مقاله كرانهاي جديدي براي اين پايا ارايه شده است.

The Wiener polarity index Wp(G) of a molecular graph G of order n is the number of unordered pairs of vertices u, v of G such that the distance d(u,v) between u and v is 3. In an earlier paper, some extremal properties of this graph invariant in the class of catacondensed hexagonal systems and fullerene graphs were investigated. In this paper, some new bounds for this graph invariant are presented. A relationship between Wiener and Wiener polarity index of some classes of graphs are also presented.