CONNECTED GRAPHS OF DIAMETER TWO HAVING SMALL DEGREE DISTANCES

IOAN TOMESCU Faculty of Mathematics and Computer Science, University of Bucharest, Str. Academiei, 14, 010014 Bucharest, Romania, e-mail: ioan@fmi.unibuc.ro

Topological indices, like degree distance, introduced by Dobrynin and Kochetova and Gutman were studied in mathematical chemistry. In this paper it is proved that in the class of connected graphs G of order n â‰Ą 4 and diameter equal to 2 such that G not â‰…K_{1,n-1}, the minimum degree distance is reached by K_{1,n-1} + e and it is conjectured that the bistar consisting of vertex disjoint stars K_{1,n-3} and K_{1,1} with central vertices joined by an edge has minimum degree distance in the class of connected graphs G of order n such that G not â‰… K_{1,n-1}.