The Bounds Of PI Index Of Polyomino Chains Of 2k-Cycles And Extremal Wiener Index Of Multiphenyl Spiders Chains

The structure of a molecule could be represented in a variety of ways. The information onthe chemical constitution of molecule is conventionally represented by a molecular graph. Andgraph theory was successfully provided the chemist with a variety of very useful tools, namely,topological indices. One of the oldest and most thoroughly examined molecular graph-basedstructural descriptor of organic molecule is the Wiener index or Wiener number. Given an edgee∈E(G) of G. we define the distance of e to a vertex w∈V(G) as the minimum of the distanceof its edges to w. i.e.,d(w, e) = min{d(w, u), d(w, v)}. Let us denote the number of edges lyingcloser to the vertex u than the vertex v of e by neu(e|G) and the number of edges lying closerto the vertex v than the vertex u by nev(e|G). Thus neu(e|G) = |{f∈E(G)|d(u, f) < d(v, f)}| .and similarly for nev(e|G). The Padmakar - Ivan(PI) index of a graph G is defined as PI(G) = . The distance between vertices u and v of G is denoted by dG(u, v).The Wienerindex of G is denoted by W(G) and is defined by .The first chapter intended as introduction to basic concepts and terminations of graphs,together with the background on Wiener index and PI index. In chapter 2, we show that multi-phenyl spider chains can attain the extremal values of Wiener index. In chapter 3, we attain theresults to the case of k-polyomino chains for arbitrary k.