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Graph operations on the symmetric division deg index of graphs. (English) Zbl 1346.05245

Summary: The symmetric division deg index of a connected graph \(G\), is defined as \(\mathrm{SDD}(G)= \sum_{uv \in E(G)}\frac{d_u}{d_v}+\frac{d_v}{d_u}\) where \(d_v\) is the degree of a vertex \(v\) in \(G\). In this paper, we concentrated on the graph operations like lexicographic product, symmetric difference and corona product of graphs related to the symmetric division deg index.

MSC:

05C76 Graph operations (line graphs, products, etc.)
05C07 Vertex degrees
05C35 Extremal problems in graph theory
05C25 Graphs and abstract algebra (groups, rings, fields, etc.)
05C20 Directed graphs (digraphs), tournaments
05C05 Trees
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