AN INTRODUCTION TQ GEODETIC POLYNOMIAL OFA GRAPH

摘要

We introduce a new geodetic polynomial of a graph G. The -geodetic polynomial of a graph G of order n is the polynomial g(G,x)= ∑g_e(G,i)x~i, where g_e(G,i)is the number of 1=g(G), geodetic sets of G of size i and g(G) is the geodetic number of G.. We obtain some properties of g {G,x) and its coefficients. Also, we compute the polynomial for some specific graphs.