Abstract
The omega polynomial Ω(G,x), for counting qoc strips in molecular graph G was defined by Diudea as with m(G,c), being the number of qoc strips of length c. The Theta polynomial Θ(G,x) and the Theta index Θ(G) of a molecular graph G were defined as Θ(G,x)= and Θ(G)=, respectively.In this paper, we compute the Theta polynomial Θ(G,x) and the Theta index Θ(G) of molecular graph Polycyclic Aromatic Hydrocarbons PAHk, for all positive integer number k.
Highlights
Let G be a simple molecular graph without directed and multiple edges and without loops, the vertex and edge-sets of which are represented by V(G) and E(G), respectively
In a plane bipartite graph, an edge e is in relation θ with any opposite edge f if the faces of the plane graph are isometric
An orthogonal cut oc with respect to a given edge is the smallest subset of edges closed under this operation and C(e) is precisely a θ-class of G
Summary
Let G be a simple molecular graph without directed and multiple edges and without loops, the vertex and edge-sets of which are represented by V(G) and E(G), respectively.A graph can be described by a connection table, a sequence of numbers, a matrix, a polynomial or by a single number (often called a topological index). Let G be a simple molecular graph without directed and multiple edges and without loops, the vertex and edge-sets of which are represented by V(G) and E(G), respectively. M(G,k) X k k with the exponents showing the extent of partitions p(G), p(G)=P(G) of a graph property P(G) while the coefficients m(G, k) are related to the number of partitions of extent k.
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