STRUCTURAL PROPERTIES OF I-GRAPHS: THEIR INDEPENDENCE NUMBERS AND CAYLEY GRAPHS

Abstract

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.