Abstract
The status of a vertex x in a graph is the sum of the distances between x and all other vertices. The status sequence of a graph is the list of the statuses of all vertices arranged in nondecreasing order. It is well known that non-isomorphic trees may have the same status sequence. We show that a tree is uniquely determined by its status sequence if the only pairs of vertices that have the same status are endvertices.
Original language | English |
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Pages (from-to) | 133-143 |
Number of pages | 11 |
Journal | Ars Combinatoria |
Volume | 139 |
Publication status | Published - 2018 Jul |
Keywords
- Status
- Status injective graph
- Status sequence
- Status unique graph
- Tree
- Weakly status injective tree
ASJC Scopus subject areas
- General Mathematics