Advances and Applications in Discrete Mathematics
Volume 22, Issue 1, Pages 1 - 40
(September 2019) http://dx.doi.org/10.17654/ |
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SIMPLE GRAPHOIDAL COVER ON TENSOR PRODUCT OF GRAPHS
G. Venkat Narayanan, J. Suresh Suseela and R. Kala
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Abstract: A graphoidal cover of G is a set 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. If every two paths in ψ have at most one common vertex, then it is called a simple graphoidal cover of G. The minimum cardinality of a simple graphoidal cover of G is called a simple graphoidal covering number of G and is denoted by ηs. Here we determine the ηs on tensor product of graphs. |
Keywords and phrases: graphoidal covers, simple graphoidal covers, tensor product of graphs.
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