Bulletin of Pure & Applied Sciences- Mathematics and Statistics
Year: 2012
Volume: 31e
Issue: 1
An introduction to geodetic polynomial of a graph
Author:
A. Vijayan, T. Binu Selin1
Total Page Count: 8
Page Number: 25 to 32
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.
Abstract
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.
