On (2,1)-Total Labelings of Categorical Products of Two Cycles

A (p, 1)-total labeling of a graph 'G' is an assignment of 'V (G) ∪ E(G)' to integers such that any two adjacent vertices of 'G' receive distinct integers, any two adjacent edges of 'G' receive distinct integers and a vertex and its incident edges receive integers that differ by at least 'p' in absolute value. The ('p', 1)-'total number' of a graph 'G' is the width of the smallest range of integers that suffices to label the vertices and edges of 'G' to obtain a ('p', 1)-total labeling for 'G'. In this paper, we have determined the exact value of the (2, 1)-total number of the categorical product of 'G' and 'H', no matter 'G' and 'H' is any cycle or path.