Degree Distance Index of the Mycielskian and its Complement

در اين مقاله ما مقدار دقيق شاخص فاصله-درجه مكمل ميسيليسكي گراف هاي دلخواه را مشخص مي‌نماييم. قضيه مشهوري وجود دارد مبني بر اين كه با ديد احتمالاتي تقريبا همه گراف ها با قطر دو هستند. بر اين اساس شاخص فاصله-درجه را براي ميسيليسكي گراف هاي با قطر دو مشخص مي‌كنيم.

Let G be a finite connected simple graph. The degree distance index ) (G DD of G is defined as ? ? ? ) ( } , { )) ( deg ) ( )(deg , ( G V v u v G u G v u G d , where ) ( deg u G is the degree of vertex u in G and ) , ( v u G d is the distance between two vertices u and v in G . In this paper, we determine the degree distance of the complement of arbitrary Mycielskian graphs. It is well known that almost all graphs have diameter two. We determine this graphical invariant for the Mycielskian of graphs with diameter two.