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The edge geodetic number and Cartesian product of graphs

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Santhakumaran A., Ullas Chandran S.

Discussiones Mathematicae Graph Theory

2010

tom 30

nr 1

55-73

For a nontrivial connected graph G = (V(G),E(G)), a set S⊆ V(G) is called an edge geodetic set of G if every edge of G is contained in a geodesic joining some pair of vertices in S. The edge geodetic number g₁(G) of G is the minimum order of its edge geodetic sets. Bounds for the edge geodetic number of Cartesian product graphs are proved and improved upper bounds are determined for a special class of graphs. Exact values of the edge geodetic number of Cartesian product are obtained for several classes of graphs. Also we obtain a necessary condition of G for which g₁(G ☐ K₂) = g₁(G).

Ograniczanie wyników

1 Discussiones Mathematicae Graph Theory

1 Santhakumaran A.

1 Ullas Chandran S.

1 2010

Wyniki wyszukiwania

The edge geodetic number and Cartesian product of graphs