Abstract

On The Tree and Star Numbers of A Graph

V. R. Kulli and S. C. Sigarkanti

Department of Mathematics Gulbarga University, Gulbaraga, INDIA. Department of Mathematics Government Science College, Bangalore, INDIA

ABSTRACT

The tree number t(G) of a graph G is the minimum number of subsets into which the edge set of G can be partitioned so that each subset induces a tree. The star number s(G) of a graph G is the minimum number of subsets into which the edge set of G can be partitioned so that each subset induces a star. In this paper, the exact values of t(G) and s(G) for some standard graphs are obtained. Bounds on these parameters are established. Also Nordhaus- Gaddum type results for the star number are established. Mathematics subject Classification: 05C

Keywords :tree number, star number, path number.

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