Abstract: The
bandwidth of a graph Gis the minimum of the quantity taken
over all injective integer numberings fof G. The tensor product of two graphs Gand H, written as is the graph with vertex set and with adjacent to if is adjacent to in Gand is adjacent to in H. In this paper, we
investigate the bandwidth of the tensor product of two connected graphs. We
denote the minimum degree of a graph Hby For a vertex xof a graph Hand a
non-negative integer i, let denote the set of vertices ysuch that there exists an
-walk of length iin H. We define
for positive integers j. Let Gbe a k-connected graph and let Hbe a connected graph of order nand diameter dsuch
that there is an
-walk of length dfor every (not necessarily distinct) vertices xand yof H. Among other results, we prove that if then Moreover, we show that this result
determines the bandwidth of the tensor product of some classes of graphs.
Keywords and phrases: bandwidth, tensor product, connectivity, diameter, distance.
