Article ID Journal Published Year Pages File Type
4601914 Linear Algebra and its Applications 2010 18 Pages PDF
Abstract

Using the AutoGraphiX system, we obtain conjectures of the form l(n)⩽q1⊕i(G)⩽u(n) where q1 denotes the signless Laplacian index of graph is one the four operations is another invariant chosen among minimum, average and maximum degree, average distance, diameter, radius, girth, proximity, remoteness, vertex, edge and algebraic connectivities, independence number, domination number, clique number, chromatic number and matching number, Randić index, l(n) and u(n) are best possible lower and upper bounds function of the order n of G. Algebraic conjectures are obtained in 120 cases out of 152 and structural conjectures in 12 of the remaining cases. These conjectures are known, immediate or proved in this paper, except for 17 of them, which remain open.

Related Topics
Physical Sciences and Engineering Mathematics Algebra and Number Theory