Abstract
Using the AutoGraphiX 2 system (AGX2), we study relations between graph invariants of the form b n ≤ g ⊗ i ≤ b n where g denotes the girth of a graph G = (V, E), i another invariant among the average distance l, the index λ 1 , the Randic index R and the domination number β, ⊗ denotes one of the four operations +, -, ×, /, b n and b n lower and upper bounding functions of the order n of the graph considered which are tight for all n (except possibly very small values due to border effects). The results proved or discussed below were first presented as conjectures in a previous paper published in RAIRO Operations Research [RAIRO Oper. Res. 39 (2005) 275-293].
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