ARITHMETIC ODD DECOMPOSITION OF SPIDER TREE

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N. Gnanadhas, E. E. R. M. (2013). ARITHMETIC ODD DECOMPOSITION OF SPIDER TREE. Asian Journal of Current Engineering and Maths, 2(2). Retrieved from http://innovativejournal.in/index.php/ajcem/article/view/155
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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)E(G2)…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. A decomposition (G1, G2, …, Gn)of  G is said to be Arithmetic decomposition(AD) if |E(Gi)| = a+ (i-1)d for every i=1, 2, 3, …, n and a, dÎZ+. An arithmetic odd decomposition (AOD) is an arithmetic decomposition with a = 1 and d = 2. We denote the AOD by (G1, G3, …, G2n-1). In this paper we study the AOD of spider tree.

 

AMS Subject Classification: 05C99.

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