ON MONOPOLYNOMIALS OF PATHS

There are some well-known polynomials in Graph theory 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 parameter 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 influence such as a disease or a belief in social networks.

Domination, domination polynomial, monopolynomial.