Michel Mollard

Power Domination in Product Graphs

The power system monitoring problem asks for as few as possible measurement devices to be put in an electric power system. The problem has a graph theory model involving power dominating sets in graphs. The power domination number

On domination numbers of Cartesian product of paths

\gamma_P(G)

On the Non-existence of 3-Dimensional Tiling in the Lee Metric

of

A linear algorithm for minimum 1-identifying codes in oriented trees

G

Disjoint cycles and spanning graphs of hypercubes

is the minimum cardinality of a power dominating set. Dorfling and Henning [Discrete Appl. Math., 154 (2006), pp. 1023-1027] determined the power domination number of the Cartesian product of paths. In this paper the power domination number is determined for all direct products of paths except for the odd component of the direct product of two odd paths. For instance, if

New results on variants of covering codes in Sierpiński graphs

n

Variations on Tilings in the Manhattan Metric

is even and

Spanning caterpillars of a hypercube

C

Two characterizations of generalized hypercube

a connected component of

On disjoint hypercubes in Fibonacci cubes

P_m\times P_n