By submitting this extended abstract to IMC44 I confirm that (i) I and any other coauthor(s) are responsible for its content and its originality; (ii) any possible coauthors agreed to its submission to IMC44. ON MONOPOLYNOMIALS OF PATHS NAHIDEH ASADI 1* ; FARIDEH KHOEINI 2 Department of Pure Mathematics, Institute for Advanced Studies in Basic Sciences (IASBS), P. O. Box 1159, Zanjan, 45195, Iran; 1 n.asadi@iasbs.ac.ir 2 samirakhoeiny@yahoo.com Abstract. There are some well-known polynomials in Graph the- ory including chromatic and independence polynomials. Recently, [Alikhani and Peng, 2009] have defined the domination polynomial as well, few applications of which are: (a) We can find the number of dominating sets of each size of a graph. (b) Since D(G, 1) is the number of all dominating sets of a graph, so we have this parame- ter which is useful for a computer scientist. (c) By this polynomial we are able to study some of geometrical properties of graphs. The phenomena of the spread of influence occur in social networks. Graph theory is frequently used for modeling social networks in general, and this phenomenon is formulated by the concept of dynamic monopolies which are in fact a modeling for irreversible spread of inuence such as a disease or a belief in social networks. 1. Introduction First, we need to define a domination set. A set D of vertices in G is a dominating set for G if every vertex of V (G) \ D is adjacent to some vertex of D. The minimum cardinality of a dominating set of G 2010 Mathematics Subject Classification. Primary 47A55; Secondary 39B52, 34K20, 39B82. Key words and phrases. Domination, domination polynomial, monopolynomial. * Speaker. 1