1Department of Mathematics, Marthandam College of Engineering and Technology, Kuttakuzhi, Kanyakumari District, Tamil Nadu, India. Email: binuselin@gmail.com
Department of Mathematics, Nesamony Memorial Christian College, Marthandam-629165, Kanyakumari District, Tamil Nadu, India. Email: naacnmccm@gmail.com
Online published on 11 January, 2013.
We introduce a new geodetic polynomial of a graph G. The geodetic polynomial of a graph G of order n is the polynomial , where ge(G,i) is the number of geodetic sets of G of size i and g(G) is the geodetic number of G. We obtain some properties g(G,x) and its coefficients. Also, we compute the polynomial for some specific graphs.
Geodetic polynomial, Geodetic set, Geodetic number, Unimodal
