16572

16572

گراف هاي فاصله متوازن تعميم يافته

دكتري

رياضي محض - جبر

آذر 1395

پروفسور مهدي علائيان

رياضي

1395/11/19

1/1/1900 12:00:00 AM

Abstract: This thesis studies on distance balanced graphs an​d its extension. At the first, the family of distance balanced graphs are given an​d investigate two subsets strongly distance balanced an​d nicely distance balanced graphs. By generalizing the concept of distance balanced graphs on path of length n instead of edge, we introduce n-distance balanced graphs an​d obtain some of its properties. Specially, strongly 2-distance balanced an​d nicely 2-distance balanced graphs are introduced an​d we explain the advantages of the new extension with mention some examples an​d rules. Then we investigate perfect codes on some distance balanced graphs an​d introduced distance balanced codes. In order to consider applications of distance balanced graphs, we express its relation with equal pportunity networks an​d present some examples with the aim of optimization. Finally, the concept of defensive alliance in graph is given an​d we fined defensive alliance number of some distance balance graphs. Keywords: Distance balanced graph, n-distance balanced graph, Strongly distance balanced graph, Nicely distance balanced graphs, Distance balanced code.