On the Symmetric Division Deg Coindex

Let G be a graph of minimum degree at least 1.Denote by di the degree of a vertex vi in G.The notation i j is used to indicate that the vertices vi and vj are not adjacent in G.A graph of maximum degree at most 4 is known as a molecular graph.A connected graph having the same order and size is called a unicyclic graph.The symmetric division deg coindex of G is defined asIn this paper, new bounds for the coindex SDD(G) as well as relations between SDD(G) and some other topological indices/coindices are obtained.From one of the obtained results, it follows that the star graph (cycle graph, respectively) uniquely minimizes symmetric division deg coindex among all trees ((molecular) unicyclic graphs, respectively) of a given order.