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A subset of n tuples of elements of Z9 is said to be a code over Z9 if it is a Z9-module. In this paper we consider an special family of cyclic codes over Z9, namely quadratic residue codes. We define these codes in term of their idempotent generators and show that these codes also have many good properties which are analogous in many respects to properties(More)
Abstract: The Hosoya polynomial of a molecular graph G is defined as ∑ ⊆ = ) ( } , { ) , ( ) , ( G V v u v u d G H λ λ , where d(u,v) is the distance between vertices u and v. The first derivative of H(G,λ) at λ = 1 is equal to the Wiener index of G, defined as ∑ ⊆ = ) ( } , { ) , ( ) ( G V v u v u d G W . The second derivative of ) , ( 2 1 λ λ G H at λ = 1(More)
The Wiener index W (G) of a connected graph G is defined as the sum of distances between all pairs of vertices. The Wiener polynomial H(G, x) has the property that its first derivative evaluated at x = 1 equals the Wiener index, i.e. H (G, 1) = W (G). The hyper-Wiener polynomial H H(G, x) satisfies the condition H H (G, 1) = W W (G), the hyper-Wiener index(More)