Structural Properties Of I-Graphs: Their Independence Numbers And Cayley Graphs

We discuss in this paper the independence numbers and algebraic properties of I-graphs. The I-graphs are a further generalization of the Generalized Petersen graphs whose independence numbers have been previously researched. Specifically, we give bounds for the independence number of different I-graphs and sub-classes of I-graphs, and exactly determine the independence number for other I-graphs and sub-classes of I-graphs. We also analyze the automorphism groups of the I-graphs. These groups have been characterized in previous papers in this paper, we examine them via their Cayley graphs. These Cayley graphs are characterized completely and examined according to their graph theoretical and algebraic properties.