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{set minus}. S than in S. A bipartition π= {S, V{set minus}. S} is called very cost effective if both S and V{set minus}. 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.
| Identifer | oai:union.ndltd.org:ETSU/oai:dc.etsu.edu:etsu-works-16629 |
| Date | 01 November 2015 |
| Creators | Haynes, Teresa W., Hedetniemi, Stephen T., Vasylieva, Inna |
| Publisher | Digital Commons @ East Tennessee State University |
| Source Sets | East Tennessee State University |
| Detected Language | English |
| Type | text |
| Source | ETSU Faculty Works |
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