Odd Star Decomposition of Lobster

Abstract

Let G = (V, E) be a simple connected graph with p vertices and q edges. If G1, G2, …, Gn are connected edge disjoint subgraphs of G with E(G)=E(G1) \(\displaystyle \cup\) E(G2)\(\displaystyle \cup\) … \(\displaystyle \cup\)E(Gn), then (G1, G2, …, Gn) is said to be a decomposition of G. A decomposition (G1, G2, …, Gn) of G is said to be continuous monotonic decomposition (CMD) if each Gi is connected and |E(Gi)|=i, for every i=1, 2, 3, …, n. In this chapter, we introduced the concept Odd Star Decomposition of Lobster graph L and discussed several theorems based on diam (L).