Symmetry properties of generalized graph truncations

dynamic coloring of graph

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 ...

Graph Properties in Node-Query Setting: Effect of Breaking Symmetry

The query complexity of graph properties is well-studied when queries are on edges. We investigate the same when queries are on nodes. In this setting a graphG = (V ,E)on n vertices and a propertyP are given. A blackbox access to an unknown subset S ⊆V is provided via queries of the form ‘Does i ∈ S?’. We are interested in the minimum number of queries needed in worst case in order to determine...

Generalized symmetry of graphs

Symmetry of graphs has been extensively studied over the past 50 years by using automorphisms of graphs and group theory which have played an important role in graph, and promising and interesting results have been obtained[2,20,21]. We introduced generalized symmetry of graphs and investigated it by using endomorphisms of graphs and semigroup theory. In this paper, I will survey some results w...

Properties of Generalized Berwald Connections

The Generalized DCell Network Structures and Their Graph Properties

DCell [7] has been proposed as a server centric network structure for data centers. DCell can support millions of servers with high network capacity and provide good fault tolerance by only using commodity mini-switches. In this paper, we show that DCell is only a special case of a more generalized DCell structure. We give the generalized DCell construction rule and several new DCell structures...