On the Radio Number of Square of Graphs

Motivated by problems in radio channel assignment, we consider the radio k-coloring of graphs. Our goal is to minimize the span of the radio k-coloring. We present an upper and a lower bound for radio number of graphs which are square of some graphs. For an n-vertex simple connected graph, the difference between the upper and lower bounds is at most . Also, we determine the radio number for square of graphs belonging to some specific class and applying this we find the same for square of hypercube , square of toroidal grid and square of some generalized prism graphs.