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Recently introduced Zagreb coindices are a generalization of classical Zagreb indices of chemical graph theory. We explore here their basic mathematical properties and present explicit formulae for these new graph invariants under several graph operations .

We introduce a modification of the Harary index where the contributions of vertex pairs are weighted by the sum of their degrees. After establishing basic mathematical properties of the new invariant, we proceed by finding the extremal graphs and investigating its behavior under several standard graph products.

A secondary structure is a planar, labeled graph on the vertex set {1; : : : ; n} having two kind of edges: the segments [i; i + 1], for 1 6 i 6 n − 1 and arcs in the upper half-plane connecting some vertices i; j, i 6 j, where j − i ¿ l, for some ÿxed integer l. Any two arcs must be totally disjoint. We enumerate secondary structures with respect to their… (More)

Valence-weightings are considered for shortest-path distance moments, as well as related weightings for the so-called " Wiener " polynomial. In the case of trees the valence-weighted quantities are found to be expressible as a combination of unweighted quantities. Further the weighted quantities for a so-called " thorny " graph are considered and shown to… (More)

Two general methods for establishing the logarithmic behavior of recursively defined sequences of real numbers are presented. One is the interlacing method, and the other one is based on calculus. Both methods are used to prove logarithmic behavior of some combinatorially relevant sequences, such as Motzkin and Schröder numbers, sequences of values of some… (More)

The Narumi-Katayama index of a graph G, denoted by NK(G), is equal to the product of the degrees of the vertices of G. In this paper we compute this index for Splice and Link of two graphs. At least with use of Link of two graphs, we compute this index for a class of dendrimers. With this method, the NK index for other class of dendrimers can be computed… (More)

We consider four classes of graphs arising from a given graph via different types of edge subdivisions. We present explicit formulas expressing their eccentric connec-tivity index in terms of the eccentric connectivity index of the original graph and some auxiliary invariants.