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Wireless Networks Analysis based on Graphs with Equal and Strong Proper Connection Number

An edge colored graph is properly colored if there exists a proper path (a path in which two neighboring edges do not acquire identical color) amid every two distinct vertices. Such a graph is called a properly connected graph and such a coloring of the graph G is called a properly connected coloring. The proper connection number of G is the least number of colors essential for a properly connected coloring of G and is symbolized as pc(G). The strong proper connection number, represented by spc(G) is the least possible number of colors necessary to color the edges of G so that amid every two vertices, there is a shortest proper path. In this article, graphs with equal proper connection numbers and strong proper connection have been investigated.