Browsing College of Arts & Sciences by Publisher "Charles Babbage Research Centre"
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A new upper bound of the basis number of the lexicographic product of graphs
( Charles Babbage Research Centre , 2010 , Article)An upper bound of the basis number of the lexicographic product of two graphs from the basis number of the factors is presented. Furthermore, the basis numbers of the lexicographic product of some classes of graphs is determined. -
On the basis number of the wreath product of ladders
( Charles Babbage Research Centre , 2016 , Article)The basis number of a graph G is defined to be the least non negative integer d such that there is a basis B of the cycle space of G such that each edge of G is contained in at most d members of B. In this paper, we determine ... -
On the basis number of the wreath product of paths with wheels and some related problems
( Charles Babbage Research Centre , 2017 , Article)In this paper, we investigate the basis number for the wreath product of wheels with paths. Also, as a related problem, we construct a minimum cycle basis of the same. -
The theta-complete graph Ramsey number R(θn K5) = 4n - 3 for n = 6 and n≥ 10
( Charles Babbage Research Centre , 2017 , Article)For any two graphs F1 and F2, the graph Ramsey number r(F1, F2) is the smallest positive integer N with the property that every graph of at least N vertices contains F1 or its complement contains F2 as a subgraph. In this ...