Extremal embedded graphs

Eccentric Connectivity Index: Extremal Graphs and Values

Eccentric connectivity index has been found to have a low degeneracy and hence a significant potential of predicting biological activity of certain classes of chemical compounds. We present here explicit formulas for eccentric connectivity index of various families of graphs. We also show that the eccentric connectivity index grows at most polynomially with the number of vertices and determine ...

Extremal Stable Graphs

Extremal graphs for weights

Extremal Graphs in Connectivityaugmentationtibor

Let A(n; k; t) denote the smallest integer e for which every k-connected graph on n vertices can be made (k + t)-connected by adding e new edges. We determine A(n; k; t) for all values of n; k and t in the case of (directed and undirected) edge-connectivity and also for directed vertex-connectivity. For undirected vertex-connectivity we determine A(n; k; 1) for all values of n and k. We also de...

Acquisition-extremal graphs

A total acquisition move in a weighted graph G moves all weight from a vertex u to a neighboring vertex v, provided that before this move the weight on v is at least the weight on u. The total acquisition number, at(G), is the minimum number of vertices with positive weight that remain in G after a sequence of total acquisition moves, starting with a uniform weighting of the vertices of G. For ...