Theset of vertices ( ) and set of edges ( ) forms a mathematical structure, which is called graph . A -coloring of a graph = ( , ) is a coloring : → such that, for each in , there exists some vertex in ( ) which is colored by and = \{ }.In this paper, we give the exact value for the -chromatic number of triangular snake graph and middle graph of triangular snake graph, which is denoted by and T n respectively.

The main purpose of this paper is to prove some fixed point theorems and its applications in partial and generalized partial cone metric spaces. Our results are satisfying various contractive conditions on cone spaces. We also prove the uniqueness of such fixed points theorems.

Graph theory has many applications in computer science. But it can also be used to make the data secure. Sometime it is used in networking for many purposes. Cloud computing provide user many services like SAAS, IAAS and PAAS. But with many benefit still cloud providers are not too much confident about the security aspects. As for the data storage, cloud data center depends upon third party involvement. So there is need of an algorithm that can authenticate sender and receiver before any transaction between user and third party. The Proposed algorithm uses the adjacency matrix to make the data secure. OTP is one of the attractions used before any transaction.

S. The theory has several rather well-defined (yet overlapping) branches. The purely topological theory as well as those topics which lie on the borderline of topology and functional analysis (e.g. those related to Leray-Schauder theory) have their roots in the celebrated theorem of L. E. J. Brouwer. This paper presents a review of the available literature on fixed point theorems for various types of maps.