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For a simple undirected graph spread is defined as the difference between the largest and the smallest eigenvalue of the graph. As 1 is the largest eigenvalue of the Randić matrix therefore disregarding the spectral radius, the Randić spread is the difference between the second largest and the smallest eigenvalue of the Randić matrix. In this communication we have studied the bounds for Randić spread. Moreover we have introduced a new upper and lower bound for this spread.

For a graph G = (V,E) and a finite set T of positive integers containing zero, ST-coloring of a graph G is a coloring of the vertices with non negative integers such that for any two vertices of an edge, the absolute differences between the colors of the vertices does not belong to a fixed set T of non negative integers containing zero and for any two distinct edges their absolute differences between the colors of their vertices are distinct. The minimum number of colors needed for an efficient Strong T coloring of a graph is known as ST-Chromatic number. This communication is concerned with the ST-coloring of some non perfect graphs viz. Petersen graph, Double Wheel graph, Helm graph, Flower graph, Sun Flower graph. We compute ST-chromatic number of these non perfect graphs.