Computing eccentricity based topological indices of octagonal grid \(O_n^m\). (English) Zbl 1401.05077
Summary: 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 \(\varepsilon_v\) 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 \(C^\xi(G) = \sum_{v \in V(G)} d_v / \varepsilon_v\), eccentric connective index \(\xi(G) = \sum_{v \in V(G)} d_v \varepsilon_v\) and eccentric Zagreb index of octagonal grid \(O_n^m\), where \(d_v\) represents the degree of the vertex \(v\) in \(G\).
MSC:
| 05C07 | Vertex degrees |
| 05C12 | Distance in graphs |
| 05C38 | Paths and cycles |
| 05C90 | Applications of graph theory |
| 92E10 | Molecular structure (graph-theoretic methods, methods of differential topology, etc.) |
Keywords:
eccentric connective index; connective eccentric index; eccentric Zagreb index; the octagonal grid \(O_n^m\)References:
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