Geometric Decomposition of Spider Tree

Let G = (V E) be a simple connected graph with p vertices and q edges. If G1 G2 G3 Gn are connected edge disjoint subgraphs of G with E (G) = E (G1) E (G2) E (G3) E (Gn) then (G1 G2 G3, Gn) is said to be a decomposition of G. A decomposition (G1 G2 G3 Gn) of G is said to be an Arithmetic Decomposition if each Gi is connected and |E (Gi) | = a + (i -1) d, for every i = 1 2 3n and a d. In this paper we introduced a new concept Geometric Decomposition. A decomposition (Ga Gar Gar2 Gar3 Garn-1) of G is said to be a Geometric Decomposition (GD) if each Gari-1 is connected and |E (Gari-1) | = ari-1, for every i = 1 2 3n and a r. Clearly q =. If a = 1 and r = 2 then q = 2n-1. In this paper we study the Geometric Decomposition of spider tree.