Perfect coloring of graphs and related aspects

Abstract

The theory of graphs and its humongous applications have increased over the last few decades. newlineThe rise of automation and computerisation has developed the research on this topic. Graph newlinetheory has diversified applications in various fields like electrical engineering, computer newlinescience, etc. Graphs describe any complicated situation to simpler one. Hence graph theory is newlinean essential part of applied mathematics. newlineThe graph theory was initiated with an important Konigsberg Bridge (KB) problem in 1735. newlineThis was the most difficult problem of those days. Euler is said to be the father of the theory newlineof graphs when he solved this KB Problem in 1736. This was the first problem of the graph newlinetheory. He solved this problem by plotting a graph. This problem introduced the planar graphs newlineand Eulerian graphs. In this way, the new types of graphs were introduced by different newlinemathematicians in the next century. The mathematician Mobius introduced bipartite and newlinecomplete graphs in 1840. G Kirchhoff developed the idea of trees in 1845. These trees are newlinehelpful in solving electrical network and circuit problems, developed this in calculating newlinecurrents in an electrical network[1].