Abstract:

For a simple and connected graph G, denote the domination number, the
diameter, and the radius of G as β(G), D(G), and r(G), respectively. In this paper,
we solve two conjectures on the upper bounds of β(G) · D(G) and β(G) + r(G),
which are proposed by the computer system AutoGraphiX. Extremal trees which
attain the upper bounds are also considered.

Key words: Auto GraphiX , Upper bounds , Extremal tree , Domination number