The discrete isoperimetric problem on G is to find the value of [b.sub.e](i, G), for each i, 1 [less than or equal to] i [less than or equal to] i [absolute value of V(G)].

The discrete connected isoperimetric problem on G is to find the value of [b.sub.c](i, G), for each i, 1 [less than or equal to] i [less than or equal to] [absolute value of V(G)].

Theorem 1.1 is used in [2] to relate the Tanny value to connected discrete isoperimetric problem on [T.sub.2].

The following theorem is from [2] which relates the connected isoperimetric problem on [T.sub.2] with the boundary of the V LR tree.

Isoperimetric Problem. Let c be constant and N : D x [R.sup.3] [[right arrow] R be a continuously differentiable function with respect to its i-th argument, for i = 3,4, 5.

Torres, "

Isoperimetric problems on time scales with nabla derivatives," Journal of Vibration and Control, vol.

It contains 16 papers on such topics as travel time tubes regulating transportation traffic, quadratic growth conditions in optimal control problems, optimal spatial pricing strategies with transportation costs,

isoperimetric problems of the calculus of variations on time scales, metric regular maps and regularity for constrained extremum problems, and

isoperimetric problems of the calculus of variations on time scales, to cite a few examples.

Global methods for combinatorial isoperimetric problems.

of California, Riverside) states in the preface that "working on combinatorial isoperimetric problems, from the summer of 1962 to the present, has been the greatest aesthetic experience of my life." He started solving such problems as a research engineer at the Jet Propulsion Laboratory and believes firmly in the grounding of math in real applications.