چكيده به لاتين
Abstract:
This thesis studies on distance balanced graphs and its extension. At the first, the family of distance balanced graphs are given and investigate two subsets strongly distance balanced and 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 and obtain some of its properties. Specially, strongly 2-distance balanced and nicely 2-distance balanced graphs are introduced and we explain the advantages of the new extension with mention some examples and rules. Then we investigate perfect codes on some distance balanced graphs and introduced distance balanced codes. In order to consider applications of distance balanced graphs, we express its relation with equal pportunity networks and present some examples with the aim of optimization. Finally, the concept of defensive alliance in graph is given and 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.
