(d,1)-total Labeling Number of the Product of Path and Fan

The (d, 1)-total labeling number of a graph delta d
_d
^T
(G) is the width of the smallest range of integers that suffices to label the vertices and the edges of G such that no two adjacent vertices have the same label, no two adjacent edges have the same label and the difference between the labels of a vertex and its incident edges is at least d. In this paper, we studied the upper bound of delta d
_d
^T
(G) of the product of path and fan.