کران‌های جدیدی بر روی نسبت اطلاعات ضرب دکارتی کلاس‌هایی از گراف‌ها

نوع مقاله : مقاله پژوهشی

نویسندگان

1 دانشکده ریاضی و کامپیوتر خوانسار

2 دانشگاه شهرکرد

چکیده

در این مقاله، یک کران پایینی برای نسبت اطلاعات حاصل­ضرب دکارتی یک درخت دلخواه با قطر حداقل 3 و دور  برای هر  خواهیم یافت. علاوه براین، بهترین نسبت اطلاعات طرح تسهیم راز کامل برپایه گراف  را تعیین می­کنیم که در آن،  گراف حاصل از ضرب دکارتی دور به طول 6 با گراف مکعب است. به‌طور دقیق­تر، نشان داده می­شود که برای هر ، نسبت اطلاعات  دقیقاً برابر با  است.

کلیدواژه‌ها


عنوان مقاله [English]

Some New Bounds on the Information Ratio of the Cartesian Product of Some Classes of Graphs

نویسندگان [English]

  • Abbas Cheraghi Chaleshtari 1
  • Mohammad Gholami 2
1
2
چکیده [English]

In this paper, we find a lower-bound for the information ratio of the cartesian product of an arbitrary tree         with diameter at least  3 and a cycle Cm  for every m³3. Moreover, we determine the best information ratio of           the perfect secret sharing scheme based on the graph  constructed from the cartesian product of a cycle of  length 6 with  the d -dimensional cube Qd . More precisely, it is shown that for every d³1 , the information ratio of  is exactly
 
 

کلیدواژه‌ها [English]

  • Secret Sharing Scheme
  • Information Ratio
  • Cartesian Product
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