A Study of Graphs Decomposing Labeling, and Covering in Mathematical Graph Theory | Original Article

ABSTRACT:

A graphical label is a transfer of integrals to the vertices or edges or both, subject to certain practical conditions, labeled graphs provide useful mathematical models for a broad range of applications like theoretical coding, including the design of the best types of codes, synch set codes, missile guidance codes, convolutionary codes with an optimal auto-connection system. Graph theory applies in many fields of computer science, social science and natural science. The theory is also closely linked to numerous mathematical branches, including matrix theory, numerical analysis, probability, topology and combination. In fact, the graph theory is a mathematical component of any binary system. During the last 50 years, the theory of graphics has become an important mathematical tool for solving numerous problems. In appointing the distinct qualities of an entire number to each vertex, and then connecting the supreme distinction of these qualities to its extreme vertices, the differences in labelling in graph are recognized. Exploring the labelings for cycles, the results of two Cartesian graphs, rectangular and n-solid matrices which deteriorate the graphs into indicated pieces, are currently under consideration. The comparative issue for additional substance labels is also examined.