Graph bandwidth problem has been studies for over forty years. The relation between the bandwidth and number of edges in the graph is always interesting. The edge addition number ad(G) of a graph is the minimum number of edges that added into the graph G which cause the resulting graph’s bandwidth greater than the bandwidth of G. This paper determines the edge addition number for the Cartesian ...

We give counter-examples to the following conjecture which arose in the study of small bandwidth graphs. “For a graph G, suppose that IV(G’)( < 1 + ci . diameter (G’) for any connected subgraph G’ of G, and that G does not contain any refinement of the complete binary tree of cz levels. Is it true that the bandwidth of G can be bounded above by a constant c depending only on c, and c,?” On the ...

A modulated holding beam shining a VCSEL above threshold can improve modulation bandwidth by adjusting the semiconductor laser’s relaxation oscillation frequency. The improved modulation characteristics are accompanied by reduced damping rate. By choosing correct parameters, dynamical behavior of system and cavity solitons is changed.