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Thesis

dynamic coloring of graph

ماریا رحمانی

Abstract

در این پایان نامه رنگ آمیزی دینامیکی یک گراف را بیان و مطالعه می کنیم. یک –kرنگ آمیزی سره ی رأسی گراف g را رنگ آمیزی دینامیکی می نامند اگر در همسایه های هر رأس v?v(g) با درجه ی حداقل 2، حداقل 2 رنگ متفاوت ظاهر شوند. کوچکترین عدد صحیح k، به طوری که g دارای –kرنگ آمیزی دینامیکی باشد را عدد رنگی دینامیکی g می نامند و آنرا با نماد ?_2 (g) نمایش می دهند. مونت گمری حدس زده است که تمام گراف های منتظم در رابطه ی ?_2 (g)-?(g)?2 صدق می کنند.اکبری و بقیه ثابت کردند که تمام گراف های دو بخشی –kمنتظم و گراف های قویاً منتظم در حدس مونت گمری صدق می کنند. همچنین مونت گمری ثابت کرد اگر g یک گراف باشد به طوری که ?(g)?3، آنگاه ?_2 (g)??(g)+1. در فصل آخر تعمیمی از رنگ آمیزی دینامیکی بیان شده است.

Supervisors and advisors

نسرین سلطانخواه

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