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Edge-connectivity of strong products of graphs

100%

Bresar B., Spacapan S.

Discussiones Mathematicae Graph Theory

2007

tom 27

nr 2

333-343

The strong product G₁ ⊠ G₂ of graphs G₁ and G₂ is the graph with V(G₁)×V(G₂) as the vertex set, and two distinct vertices (x₁,x₂) and (y₁,y₂) are adjacent whenever for each i ∈ {1,2} either $x_i = y_i$ or $x_i y_i ∈ E(G_i)$. In this note we show that for two connected graphs G₁ and G₂ the edge-connectivity λ (G₁ ⊠ G₂) equals min{δ(G₁ ⊠ G₂), λ(G₁)(|V(G₂)| + 2|E(G₂)|), λ(G₂)(|V(G₁)| + 2|E(G₁)|)}. In addition, we fully describe the structure of possible minimum edge cut sets in strong products of graphs.

Some results on total domination in direct products of graphs

81%

Dorbec P., Gravier S., Klavžar S., Spacapan S.

Discussiones Mathematicae Graph Theory

2006

tom 26

nr 1

103-112

Upper and lower bounds on the total domination number of the direct product of graphs are given. The bounds involve the {2}-total domination number, the total 2-tuple domination number, and the open packing number of the factors. Using these relationships one exact total domination number is obtained. An infinite family of graphs is constructed showing that the bounds are best possible. The domination number of direct products of graphs is also bounded from below.

Ograniczanie wyników

2 Discussiones Mathematicae Graph Theory

2 Spacapan S.

1 Bresar B.

1 Dorbec P.

1 Gravier S.

1 Klavžar S.

1 2007

1 2006

Wyniki wyszukiwania

Edge-connectivity of strong products of graphs

Some results on total domination in direct products of graphs