Graphs whose line graphs are ring graphs
Given a graph H, a path of length at least two is called an H-path if meets H exactly in its ends. A graph G is a ring graph if each block of G which is not a bridge or a vertex can be constructed inductively by starting from a single cycle and then in each step adding an H-path that meets graph H i...
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| Format: | Article |
| Language: | English |
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Taylor & Francis Group
2020-09-01
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| Series: | AKCE International Journal of Graphs and Combinatorics |
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| Online Access: | http://dx.doi.org/10.1016/j.akcej.2019.10.002 |
| Summary: | Given a graph H, a path of length at least two is called an H-path if meets H exactly in its ends. A graph G is a ring graph if each block of G which is not a bridge or a vertex can be constructed inductively by starting from a single cycle and then in each step adding an H-path that meets graph H in the previous step in two adjacent vertices. In this article, we classify all graphs whose line graphs and total graphs are ring graphs. |
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| ISSN: | 0972-8600 2543-3474 |