Extremal graphs for weights

Extremal graphs for weights

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 Problems for Polynomials with Exponential Weights

For the extremal problem: E„r(a):= min||exp(-W«)(x-+ ■■■)\\L„ a > 0, where U (0 < r < oo) denotes the usual integral norm over R, and the minimum is taken over all monic polynomials of degree n, we describe the asymptotic form of the error E„ r(a) (as n -» oo) as well as the limiting distribution of the zeros of the corresponding extremal polynomials. The case r = 2 yields new information regar...

Extremal graphs for homomorphisms

The study of graph homomorphisms has a long and distinguished history, with applications in many areas of graph theory. There has been recent interest in counting homomorphisms, and in particular on the question of finding upper bounds for the number of homomorphisms from a graph G into a fixed image graph H. We introduce our techniques by proving that the lex graph has the largest number of ho...

Extremal Ramsey theory for graphs

If G and H are graphs, define the Ramsey number to be the least number p such that if the lines of the complete graph Kp are colored red and blue (say),either the red subgraph contains a copy of G or the blue subgraph contains H. Also set r(G) = r(G,G) ; these are called the diagonal Ramsey numbers. These definitions are taken from Chvátal and Harary [1J ; other terminology will follow Harary [...