Abstract
It may be possible to find the Wiener polynomial with respect to a generalized distance of a compound graph constructed from two graphs having some kind of regularity. In this paper, we obtain the Wiener polynomials for a generalized distance of compound graphs constructed from a complete graph with some other special graph, such as a complete bipartite graph, a star, and a wheel, using binary operations defined by Gutman [4]. The Wiener index with respect to such generalized distance for each such compound graph is also obtained.الملخصإن وضع صیغة لمتعددة حدود وینر لتعمیم المسافة فی البیانات المرکبة یتطلب ان تکون البیانات المرکبة لها درجة من الانتظام, وهذا ینطبق على تراکیب بعض البیانات الخاصة التی لها انتظام معین, لذلک وجدنا من المناسب إیجاد حدودیات وینر لتعمیم المسافة للبیان المرکب من البیان التام مع بعض البیانات الخاصة مثلا البیان الثنائی التجزئة التام, وبیان النجمة, وبیان العجلة بإحدى العملیات الثنائیة المعرفة لـ[4] Gutman. وکذلک أوجدنا دلیل وینر لمتعددات الحدود لتعمیم المسافة لکل من البیانات المرکبة المذکورة سابقا.
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