THE DETOUR MONOPHONIC GRPHOIDAL COVERING NUMBER OF A GRAPH
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초록
A chord of a path P is an edge joining two non-adjacent ver- tices of P. A path P is called a monophonic path if it is a chordless path. A path P is called a detour monophonic path in G if it is a longest mono- phonic path in G. A detour monophonic graphoidal cover of a graph G is a collection dm of detour monophonic paths in G such that every vertex of G is an internal vertex of at most one detour monophonic path in dm and every edge of G is in exactly one detour monophonic path in dm. The minimum cardinality of a detour monophonic graphoidal cover of G is called the detour monophonic graphoidal covering num- ber of G and is denoted by dm(G). We determine bounds for it and characterize graphs which realize the bounds. Also, we find the detour monophonic graphoidal covering number of unicyclic graphs.
Abstract
A chord of a path P is an edge joining two non-adjacent ver- tices of P. A path P is called a monophonic path if it is a chordless path. A path P is called a detour monophonic path in G if it is a longest mono- phonic path in G. A detour monophonic graphoidal cover of a graph G is a collection dm of detour monophonic paths in G such that every vertex of G is an internal vertex of at most one detour monophonic path in dm and every edge of G is in exactly one detour monophonic path in dm. The minimum cardinality of a detour monophonic graphoidal cover of G is called the detour monophonic graphoidal covering num- ber of G and is denoted by dm(G). We determine bounds for it and characterize graphs which realize the bounds. Also, we find the detour monophonic graphoidal covering number of unicyclic graphs.
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