On Graphoidal Covers of Bicyclic Graphs
نویسندگان
چکیده
A graphoidal cover of a graph G is a collection ψ of (not necessarily open) paths in G such that every path in ψ has at least two vertices, every vertex of G is an internal vertex of at most one path in ψ and every edge of G is in exactly one path in ψ. The minimum cardinality of a graphoidal cover of G is called the graphoidal covering number of G and is denoted by η(G) or η. Also, If every member in a graphoidal cover is an open path then it is called an acyclic graphoidal cover. The minimum cardinality of an acyclic graphoidal cover of G is called the acyclic graphoidal covering number of G and is denoted by ηa(G) or ηa. Here we find minimum graphoidal covering number and minimum acyclic graphoidal covering number of bicyclic graphs. Mathematics Subject Classification: 05C
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