Draw two graphs with 5 nodes that cannot be line graphs.
What will be an ideal response?
If a 4-node star graph is an induced subgraph of a graph G,then
G cannot be a line graph.
For example, Figure 2.42 of the textbook shows an example graph which is not the line graph
of any graph. That is, the 4-node star graph of Figure 2.42 consisting of nodes
V2, V3, V4, and V5 is an induced subgraph. Another example is the graph that is obtained after removing the
edge between vertices v 1 and v 5 of Figure 2.42.
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