Linkedness and Path-Pairability in the Cartesian Product of Graphs

In this dissertation I summarize my work in the field of linkedness and pathpairability of graphs with primary focus on the inheritance of the mentioned properties in the Cartesian product of graphs. We obtain a general additive inheritance bound for linkedness. We determine the exact linkedness number of hypercubes, as well as affine and projective grids of arbitrary dimensions. Similar inheritance of the path-pairability property is investigated. We show that unlike in the case of linkedness, a multiplicative lower bound can be achieved for the inharitance of path-pairability. Further results regarding maximum degree and maximum diameter conditions of path-pairable graphs are presented. In all these topics I have published, accepted or submitted papers in various mathematical journals.