ENUMERATION OF NODES DEGREE OF FINITE T- GRAPHS

Let X be a non empty set and T be a topology on it. We define a new kind of graph based on this topology T , in the way that: vertex set be the power set of X and edge set be the set of unordered pairs of nodes such that atleast one node is in topology T and intersection of the complement of this node with another one is a member of topology T. i.e., ET = {(u,v) : u ∈ T , u ≠ v & uc ∩ v ∈ T}. In this article, we associative a graph to a topology T on X , called finite T -Graph of the topology T on X . Our goal is to find the enumerations of node degrees formula for the associated graph to a topology T.