Displaying similar documents to “A splitting formula for an electromagnetic diffraction problem.”

An anti-Ramsey theorem on edge-cuts

Juan José Montellano-Ballesteros (2006)

Discussiones Mathematicae Graph Theory

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Let G = (V(G), E(G)) be a connected multigraph and let h(G) be the minimum integer k such that for every edge-colouring of G, using exactly k colours, there is at least one edge-cut of G all of whose edges receive different colours. In this note it is proved that if G has at least 2 vertices and has no bridges, then h(G) = |E(G)| -|V(G)| + 2.

Edge-domatic numbers of cacti

Bohdan Zelinka (1991)

Mathematica Bohemica

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The edge-domatic number of a graph is the maximum number of classes of a partition of its edge set into dominating sets. This number is studied for cacti, i.e. graphs in which each edge belongs to at most one circuit.

On edge detour graphs

A.P. Santhakumaran, S. Athisayanathan (2010)

Discussiones Mathematicae Graph Theory

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For two vertices u and v in a graph G = (V,E), the detour distance D(u,v) is the length of a longest u-v path in G. A u-v path of length D(u,v) is called a u-v detour. A set S ⊆V is called an edge detour set if every edge in G lies on a detour joining a pair of vertices of S. The edge detour number dn₁(G) of G is the minimum order of its edge detour sets and any edge detour set of order dn₁(G) is an edge detour basis of G. A connected graph G is called an edge detour graph if it has...