Further results on pathos graphs and related graph equations (Q2831710)
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scientific article; zbMATH DE number 6651320
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Further results on pathos graphs and related graph equations |
scientific article; zbMATH DE number 6651320 |
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10 November 2016
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pathos
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line graph
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middle graph
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Further results on pathos graphs and related graph equations (English)
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A pathos graph \(P(G)\) of a graph \(G\) is the simple graph whose vertices correspond to an edge-disjoint set of paths that cover \(G\), with an edge between two vertices if and only if the corresponding paths intersect. This paper offers characterisations, in terms of forbidden subgraphs, of when a pathos graph of a tree is a clique, bipartite, Hamiltonian, planar and outer-planar. Furthermore it determines when a pathos graph of a tree is a line graph or a middle graph.
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