Abstract
Graph theory is successfully applied in developing a relationship between chemical structure and biological activity. The relationship of two graph invariants, the eccentric connectivity index and the eccentric Zagreb index are investigated with regard to anti-inflammatory activity, for a dataset consisting of 76 pyrazole carboxylic acid hydrazide analogs. The eccentricity ε v of vertex v in a graph G is the distance between v and the vertex furthermost from v in a graph G. The distance between two vertices is the length of a shortest path between those vertices in a graph G. In this paper, we consider the Octagonal Grid O n m . We compute Connective Eccentric index C ξ ( G ) = ∑ v ∈ V ( G ) d v / ε v , Eccentric Connective Index ξ ( G ) = ∑ v ∈ V ( G ) d v ε v and eccentric Zagreb index of Octagonal Grid O n m , where d v represents the degree of the vertex v in G.
Highlights
Chemical graph theory is broadly utilized in the branch of scientific science and a few people say that chemical graph hypothesis and this hypothesis are connected with the commonsense utilizations of chart hypothesis for tackling the atomic issues
The degree of a node q in G is the quantity of line segment which is occurrence to the node q and spoken to by dq
In a chart G, if there is no reiteration of vertices in ( p − q) path such sort of path is called ( p − q) way
Summary
Chemical graph theory is broadly utilized in the branch of scientific science and a few people say that chemical graph hypothesis and this hypothesis are connected with the commonsense utilizations of chart hypothesis for tackling the atomic issues. In a associated diagram G, the eccentricity ε v of a node w is the separation amongst w and a node uttermost from w in G Along these lines, ε w = maxw∈V (G) d(w, y). A very important eccentricity based topological index of a graph G is the eccentric connectivity index ξ ( G ) which is defined as:". This topological index is used as a mathematical model to predict biological activities of diverse nature [11,12]. We consider G to be a connected graph with vertex set V ( G ) and edge set E( G ) , and compute the C ξ ( G ), ξ ( G ) and M1∗∗ ( G ) of the Octagonal grid Onm ."
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