Barbara Charchekhandra

Jadavpur University, Department Of Mathematics, Kolkata, India

Abstract

The basis number b (G) of a graph G is defined to be the smallest positive integer k such that G has a k-fold basis for its cycle space. We try to find an upper bound for .

We prove that, if and are connected vertex-disjoint graphs and each has a spanning tree of vertex degree not more than 4, then .

The basis number of quadruple join of paths will be studied, where we prove that

Keywords: Graph; Basis number; Connected vertex-disjoint graphs; Path