A STUDY OF MIXED TREE DOMINATION POLYNOMIALS IN SOME CLASS OF GRAPHS

The mixed tree domination polynomial of a connected graph G of order n is the polynomial   p⁽ⁱ⁾xⁱ, where p⁽ⁱ⁾ is the number of mixed tree dominating sets of G of cardinality i and γ_mt(G) is the mixed tree domination number of G. We analyse the specifications of the polynomial. Also P(G, x) is determined for cycles, complete graphs and stars, and the roots of P(G, x) are studied.