Very cost effective bipartitions in graphs
For a graph G=(V,E) and a set of vertices S⊆V, a vertex v∈S is said to be very cost effective if it is adjacent to more vertices in V∖S than in S. A bipartition π={S,V∖S} is called very cost effective if both S and V∖S are very cost effective sets. Not all graphs have a very cost effective bipartiti...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Taylor & Francis Group
2015-11-01
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| Series: | AKCE International Journal of Graphs and Combinatorics |
| Subjects: | |
| Online Access: | http://www.sciencedirect.com/science/article/pii/S0972860015000365 |
| Summary: | For a graph G=(V,E) and a set of vertices S⊆V, a vertex v∈S is said to be very cost effective if it is adjacent to more vertices in V∖S than in S. A bipartition π={S,V∖S} is called very cost effective if both S and V∖S are very cost effective sets. Not all graphs have a very cost effective bipartition, for example, the complete graphs of odd order do not. We characterize the cactus graphs having a very cost effective bipartition. Also, we show that if a graph G or H has a very cost effective bipartition, then so does the Cartesian product G□H. |
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| ISSN: | 0972-8600 |