Abstract
We newly define a generalized vertex-ranking of a graph G as follows: for a positive integer c, a c-vertex-ranking of G is a labeling (ranking) of the vertices of G with integers such that, for any label i, every connected component of the graph obtained from G by deleting the vertices with label > i has at most c vertices with label i. Clearly an ordinary vertex-ranking is a l-vertex-ranking and vice-versa. We present an algorithm to find a c-vertex-ranking of a given tree T using the minimum number of ranks in time O(cn) where n is the number of vertices in T.
Original language | English |
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Pages (from-to) | 321-328 |
Number of pages | 8 |
Journal | Information Processing Letters |
Volume | 56 |
Issue number | 6 |
DOIs | |
Publication status | Published - 1995 Dec 22 |
Externally published | Yes |
Keywords
- Algorithms
- Generalized ranking
- Graphs
- Lexicographical order
- Trees
- Visible vertices
ASJC Scopus subject areas
- Theoretical Computer Science
- Signal Processing
- Information Systems
- Computer Science Applications