Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
6874194 | Information Processing Letters | 2018 | 4 Pages |
Abstract
An edge eâE(G) dominates a vertex vâV(G) if e is incident with v or e is incident with a vertex adjacent to v. An edge-vertex dominating set of a graph G is a set D of edges of G such that every vertex of G is edge-vertex dominated by an edge of D. The edge-vertex domination number of a graph G is the minimum cardinality of an edge-vertex dominating set of G. A subset DâV(G) is a total dominating set of G if every vertex of G has a neighbor in D. The total domination number of G is the minimum cardinality of a total dominating set of G. We prove that for every nontrivial tree T of order n, with s support vertices we have γev(T)â¤(γt(T)+sâ1)/2, and we characterize the trees attaining this upper bound.
Related Topics
Physical Sciences and Engineering
Computer Science
Computational Theory and Mathematics
Authors
Y.B. Venkatakrishnan, B. Krishnakumari,