Suborbital graphs corresponding to permutation representation of PGL(2, q)

Abstract

In this paper we construct Suborbital graphs for PGL(2,q) acting on the cosets of Cq-1 and analyze their properties. We established that the number of self paired suborbits is q + 2 and the paired suborbit are 2. Also suborbital graphs corresponding to suborbits whose elements intersect {0, ∞) at a singleton have been shown to be of girth 3. Suborbital graph corresponding to the suborbit containing (0, ∞) is found to be girth 0. Finally suborbital graph corresponding to suborbit with representative of the form (1, ßͥ ) is shown to be of girth 4.