On binary edge and maximum degree vertex labeling for simple network graphs

Abstract

In this proposed research, a graph means a non-trivial undirected simple connected graph. Using incident matrix two graceful labelings, Incident Binary Equivalent Decimal Edge Graceful Labeling, and Strong Incident Binary Equivalent Decimal Edge Graceful Labeling are defined and proved for some simple graphs and Middle Graph of simple graph. The Upper bound and Lower bound for Incident Binary Equivalent Decimal Edge Graceful Labeling is found out. In addition, the concept of Graceful labeling based on Maximum degree based vertex labeling with Odd Labeling on Edges and Maximum degree based vertex labeling with Even Labeling on Edges are observed for simple graphs. The research is progressed with the application of Graph theory in Network Topology. The Probability based approach on Data mining of Big Data in a Cloud Network is proposed for secure and cost efficient transmission of Big Data. To overcome the congestion in the connected network, the bottleneck node is analyzed to involve a minimum number of nodes for transferring data. Hops in different connected networks are proposed by Programmed Dependence Graph with a fixed source node to describe the structured level graph for any connected network to avoid traffic jams and to transmit data with a unique identification. newline