Identifying 2-Plexes in Subgraphs: A Visual Guide
Which of the following subgraphs are '2-plexes'?
[Image: https://core.xjtlu.edu.cn/pluginfile.php/535211/question/questiontext/2444812/29/1221529/Q_2plex.png]
Explanation:
A '2-plex' is a subgraph where every vertex has at least two neighbors within the subgraph. Let's analyze the provided subgraphs:
- ABCD: Vertex 'D' has only one neighbor ('C') within this subgraph. Therefore, it's not a '2-plex'.
- ABEF: All vertices have at least two neighbors within this subgraph (A has B and E, B has A and F, E has A and F, F has B and E). This is a '2-plex'.
- ADFG: Vertex 'D' has only one neighbor ('F') within this subgraph. Therefore, it's not a '2-plex'.
- BCFG: All vertices have at least two neighbors within this subgraph (B has C and F, C has B and F, F has B and C, G has B and C). This is a '2-plex'.
Answer: ABEF and BCFG are '2-plexes'.
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