Domination Sequences

Robert C. Brigham1, Julie R. Carrington2, Richard P. Vitray2
1Department of Mathematics, University of Central Florida Orlando FL 32816
2Department of Mathematical Sciences, Rollins College Winter Park FL 32789

Abstract

Let \(I(G)\) be a graphical invariant defined for any graph \(G\). For several choices of \(I\) representing domination parameters, we characterize sequences of positive integers \(a_1,a_2,\ldots,a_n\) which have an associated sequence of graphs \(G_1,G_2,\ldots,G_n\) such that \(G_i\) has \(i\) vertices, \(G_i\) is an induced subgraph of \(G_{i+1}\), and \(I(G_i) = a_i\).