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.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

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

On the basis number of the direct product of graphs

The basis number b(G) ofagraphGis defined to be the least integer d such that G has a d-fold basis for its cycle space. In this paper we: give an upper bound of the basis number of the direct product of trees; classify the trees with respect to the basis number of the direct product of trees and paths of order greater than or equal to 5; give an upper bound of the basis number of the direct product of bipartite graphs; and investigate the basis number of the direct product of a bipartite graph and a cycle.