Simon Špacapan

Connectivity of Cartesian products of graphs

Abstract Let κ ( G ) be the connectivity of G and G □ H the Cartesian product of G and H . We prove that for any nontrivial graphs G and H , κ ( G □ H ) = min { κ ( G ) | H | , κ ( H ) | G | , δ ( G □ H ) } .

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

Some results on total domination in direct products of graphs

\gamma_P(G)

ON THE EDGE-CONNECTIVITY OF CARTESIAN PRODUCT GRAPHS

of

Nonexistence of face-to-face four-dimensional tilings in the Lee metric

G

Strongly distance-balanced graphs and graph products

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

Edge-connectivity of strong products of graphs

n

Characterizing r -perfect codes in direct products of two and three cycles

is even and

On disjoint hypercubes in Fibonacci cubes

C

The Two-Coloring Number and Degenerate Colorings of Planar Graphs

a connected component of