Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4651534 | Electronic Notes in Discrete Mathematics | 2016 | 10 Pages |
Abstract
A graphoidal cover of a graph G is a set Ψ of non-trivial paths (which are not necessarily open) in G such that 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. We denote the set of all graphoidal covers of graph G by GGGG. In this paper we introduce a parameter gl(G), called graphoidal length of the graph G and is defined as gl(G)=maxΨ∈GG{minP∈Ψl(P)}gl(G)=maxΨ∈GG{minP∈Ψl(P)}. We give bounds for the parameter gl(G ) in terms of the well known and well studied parameter η(G)η(G), graphoidal covering number of the graph and show that the bounds are sharp.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Discrete Mathematics and Combinatorics
Authors
S. Arumugam, Purnima Gupta, Rajesh Singh,