On trees with total domination number equal to edge-vertex domination number plus one

An edge e ∈ E ( G ) dominates a vertex v ∈ V ( 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...

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Bibliographic Details
Published in:Proceedings of the Indian Academy of Sciences. Mathematical sciences 2016-05, Vol.126 (2), p.153-157
Main Authors: KRISHNAKUMARI, B, VENKATAKRISHNAN, Y B, KRZYWKOWSKI, MARCIN
Format: Article
Language:English
Subjects:
Mathematics
Mathematics and Statistics
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Summary:An edge e ∈ E ( G ) dominates a vertex v ∈ V ( 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 D ⊆ V ( 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 characterize all trees with total domination number equal to edge-vertex domination number plus one.
ISSN:0253-4142
0973-7685
DOI:10.1007/s12044-016-0267-6