No abstract

No abstract

A systematic method of identification of all possible structural isomers consistent with a given empirical formula is described. The method, embodied in a computer program, generates a complete list of isomers. Duplicate structures are avoided prospectively.

No abstract

No abstract

Let G be a graph. The gamma graph of G denoted by γ ⋅ G is the graph with vertex set V(γ ⋅ G) as the set of all γ-sets of G and two vertices D and S of γ ⋅ G are adjacent if and only if |D ∩ S| = γ(G) – 1. A graph H is said to be a γ-graph if there exists a graph G such that γ ⋅ G is isomorphic to H. In this paper, we show that every induced subgraph of a γ-graph is also a γ-graph. Furthermore, if we prove that H is a γ-graph, then there exists a sequence {Gn} of non-isomorphic graphs such that H = γ ⋅ Gn for every n.

For a simple connected undirected graph G, the Wiener index W (G) is defined as half the sum of all distances of the form d (u, v), where the summation is over all possible vertex pairs u, v in G. Assuming that G has more than one cut-vertex, we obtain an expression for W (G) in terms of the Wiener indices of the blocks of G and other quantities.

No abstract