The arithmetic-geometric index is a newly proposed degree-based graph invariant in mathematical chemistry. We give a sharp upper bound on the value of this ...

We investigate the ratio \(\mathcal{I}(G)\) of the average size of a maximal matching to the size of a maximum matching in a graph G. If many maximal mat...

A coloring of a graph is an assignment of colors to its vertices such that adjacent vertices have different colors. Two colorings are equivalent if they indu...

We study the average number \(A(G)\) of colors in the non-equivalent colorings of a graph \(G\). We show some general properties of this graph invariant ...

The eccentric connectivity index of a connected graph \(G\) is the sum over all vertices \(v\) of the product \(d_G(v)e_G(v)\), where \(d_G(v)\) is ...

The eccentricity of a vertex \(v\) in a graph \(G\) is the maximum distance between \(v\) and any other vertex of \(G\). The diameter of a graph `(...