Asian Journal of Mathematics and Computer Research

ENUMERATION OF NODES DEGREE OF FINITE T- GRAPHS

J. KAVITHA

Research Scholar, Department of Mathematics, Sri Venkateswara University, Tirupati, A.P 517502, India.

D. BHARATHI

2Department of Mathematics, Sri Venkateswara University, Tirupati, A.P 517502, India.

L. SREENIVASULU REDDY

Department of Mathematics, Sri Venkateswara University, Tirupati, A.P 517502, India.

*Author to whom correspondence should be addressed.

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Abstract

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., E_T = {(u,v) : u ∈ T , u ≠ v & u^c ∩ 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.

Keywords: Node, degree of a node, topology, edge, discrete topology

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