The basis number of the strong product of paths and cycles with bipartite graphs

The basis number of a graph G is defined to be the least 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. MacLane [13] proved that a graph G is planar if and only if the basis number of G is less than or equal to 2. Ali [3] proved that the basis number of the strong product of a path and a star is less than or equal to 4. In this work, (1) We give an appropriate decomposition of trees. (2) We give an upper bound of the basis number of a cycle and a bipartite graph. (3) We give an upper bound of the basis number of a path and a bipartite graph. This is a generalization of Ali's result [3].Scopu

On the Basis Number of the Strong Product of Theta Graphs with Cycles

In graph theory, there are many numbers that give rise to a better understanding and interpretation of the geometric properties of a given graph such as the crossing number, the thickness, the genus, the basis number, etc.

ON THE BASIS NUMBER OF THE COMPOSITION OF DIFFERENT LADDERS WITH SOME GRAPHS

The basis number b(G) of a graph G is defined to be the least integer k such that G has a k-fold basis for its cycle space. In this paper, we investigate the basis number of the composition of paths and cycles with ladders, circular ladders, and Möbius ladders

International Journal of Mathematical Combinatorics, Vol.2A

The International J.Mathematical Combinatorics (ISSN 1937-1055) is a fully refereed international journal, sponsored by the MADIS of Chinese Academy of Sciences and published in USA quarterly comprising 460 pages approx. per volume, which publishes original research papers and survey articles in all aspects of Smarandache multi-spaces, Smarandache geometries, mathematical combinatorics, non-euclidean geometry and topology and their applications to other sciences

International Journal of Mathematical Combinatorics, Vol.2

The International J.Mathematical Combinatorics (ISSN 1937-1055) is a fully refereed international journal, sponsored by the MADIS of Chinese Academy of Sciences and published in USA quarterly comprising 460 pages approx. per volume, which publishes original research papers and survey articles in all aspects of Smarandache multi-spaces, Smarandache geometries, mathematical combinatorics, non-euclidean geometry and topology and their applications to other sciences

On the basis number of the wreath product of ladders

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 the basis number of the wreath product of different ladders.Scopu

An upper bound of the basis number of the strong product of graphs

The basis number of a graph G is defined to be the least 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 give an upper bound of the basis number of the strong product of a graph with a bipartite graph and we show that this upper bound is the best possible