Some remarks on cyclic calcareous sedimentation as an index of climatic variations

Some remarks on the arithmetic-geometric index

Using an identity for effective resistances, we find a relationship between the arithmetic-geometric index and the global ciclicity index. Also, with the help of majorization, we find tight upper and lower bounds for the arithmetic-geometric index.

Some remarks on inverse Wiener index problem

The sum of distances between all pairs of vertices W (G) in a connected graph G as a graph invariant was first introduced by Wiener [9] in 1947. He observed a correlation between boiling points of paraffins and this invariant, which has later become known as Wiener index of a graph. Today, the Wiener index is one of the most widely used descriptors in chemical graph theory. Due to its strong co...

Some remarks on barycentric-sum problems over cyclic groups

We derive some new results on the k-th barycentric Olson constants of abelian groups (mainly cyclic). This quantity, for a finite abelian (additive) group (G,+), is defined as the smallest integer l such that each subset A of G with at least l elements contains a subset with k elements {g1, . . . , gk} satisfying g1 + · · ·+ gk = k gj for some 1 ≤ j ≤ k.

Remarks on the Wiener Polarity Index of Some Graph Operations†

TheWiener polarity indexWp(G) of a graphG of order n is the number of unordered pairs of vertices u and v of G such that the distance dG(u, v) between u and v is 3. In this paper the Wiener polarity index of some graph operations are computed. As an application of our results, the Wiener polarity index of a polybuckyball fullerene and C4 nanotubes and nanotori are computed. AMS Mathematics Subj...

Remarks on Cyclic Additivity