Using the AutoGraphiX 2 system (AGX2), we study further relations between graph invariants of the form lbn ≤ R ⊕ i ≤ ubn where R denotes the Randić index of a graph G = (V, E), i another invariant, ⊕ denotes one of the four operations +, -, x, /, lbn and ubn 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). Here i is in turn maximum, minimum and average degree, Δ, δ and d, diameter D, girth g, algebraic and node connectivity, a and v, Conjectures are obtained in 51 out of 56 cases, 28 of which are proved automatically, 19 are proved by hand, 7 remain open and only one is refuted.
|Number of pages||20|
|Publication status||Published - 2007|
ASJC Scopus subject areas
- Computer Science Applications
- Computational Theory and Mathematics
- Applied Mathematics