On graphoidal length of a tree in terms of its diameter
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 The graphoidal le...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Taylor & Francis Group
2020-09-01
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| Series: | AKCE International Journal of Graphs and Combinatorics |
| Subjects: | |
| Online Access: | http://dx.doi.org/10.1016/j.akcej.2019.12.012 |
| Summary: | 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 The graphoidal length gl(G) of a graph G is defined as In this paper, we obtain bounds for the graphoidal length of a tree in terms of its diameter. We prove that if G is any tree (excepts paths) of diameter d, then graphoidal length gl(G) is less than equal to Further, we characterize trees attaining the upper bound. Also, the trees for which gl(G) = k where are characterized. |
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| ISSN: | 0972-8600 2543-3474 |