• ON TOTAL EDGE FIXED GEODOMINATING SETS AND POLYNOMIALS OF GRAPHS

Abstract

We introduce total edge fixed geodomination sets and polynomial of a graph G. The total edge fixed geodomination polynomial of G is defined as Gt (G, x) = where = is the number of edge fixed geodominating sets of graph G with cardinality i, and ek is a fixed edge of G and gek (G) is the ek -geodomination number of G. we obtain some properties of Gt(G, x) and its coefficients. Also, we compute the polynomial for some specific graphs.