ON THE MONOPHONIC AND MONOPHONIC DOMINATION POLYNOMIAL OF A GRAPH

ON THE MONOPHONIC AND MONOPHONIC DOMINATION POLYNOMIAL OF A GRAPH

P. A. P. SUDHAHAR1, W. JEBI

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Abstract. A set S of vertices of a graph G is a monophonic set of G if each vertex u of G lies on an u ???? v monophonic path in G for some u; v 2 S. M  V (G) is said to be a monophonic dominating set if it is both a monophonic set and a dominating set. Let M(G; i) be the family of monophonic sets of a graph G with cardinality i and let m(G; i) = jM(G; i)j. Then the monophonic polynomial M(G; x) of G is defined as M(G; x) = Pn i=m(G) m(G; i)xi, where m(G) is the monophonic number of G. In this article, we have introduced monophonic domination polynomial of a graph. We have computed the monophonic and monophonic domination polynomials of some specific graphs. In addition, monophonic and monophonic domination polynomial of the corona product of two graphs is derived.

Keywords:Monophonic set, Monophonic Dominating set, Monophonic polynomial, Mono- phonic domination polynomial, Corona product.

AMS Subject Classification: 05C12, 05C69.