General Degree-Eccentricity Index of Trees.

For a connected graph G and a , b ∈ R , the general degree-eccentricity index is defined as DEI a , b (G) = ∑ v ∈ V (G) d G a (v) ecc G b (v) , where V(G) is the vertex set of G, d G (v) is the degree of a vertex v and ecc G (v) is the eccentricity of v in G. We obtain sharp upper and lower bounds on the general degree-eccentricity index for trees of given order in combination with given matching number, independence number, domination number or bipartition. The bounds hold for 0 < a < 1 and b > 0 , or for a > 1 and b < 0 . Many bounds hold also for a = 1 . All the extremal graphs are presented. [ABSTRACT FROM AUTHOR]