Are these two graphs isomorphic?
According to Bruce Schneier:
"A graph is a network of lines connecting different points. If two graphs are identical except for the names of the points, they are called isomorphic."
Schneier, B. "Graph Isomorphism"
From Applied Cryptography
John Wiley & Sons Inc.
ISBN 9780471117094
According to a GeeksforGeeks article:
These two are isomorphic:
And these two aren't isomorphic:
Manwani, C. "Graph Isomorphisms and Connectivity"
From GeeksforGeeks
https://www.geeksforgeeks.org/mathematics-graph-isomorphisms-connectivity/
According to a MathWorld article:
"Two graphs which contain the same number of graph vertices connected in the same way are said to be isomorphic."
Weisstein, Eric W. "Isomorphic Graphs."
From MathWorld–A Wolfram Web Resource.
http://mathworld.wolfram.com/IsomorphicGraphs.html
The details are beyond me, but the MathWorld explanation seems to conflict with the first GeeksforGeeks example; the vertices appear the same, but they appear to be connected differently.
To add to the confusion, the same could be said for the second example. So I can't really deduce the facts.
Please try to keep answers as clear and simple as possible for the sake of understanding.
"Truth is ever to be found in the simplicity, and not in the
multiplicity and confusion of things."–Isaac Newton
Best Answer
Both claims are correct.
Mapping $$e_1 \to c_1, \qquad e_2 \to c_3, \qquad e_3 \to c_5, \qquad e_4 \to c_2, \qquad e_5 \to c_4$$ maps the edges of the left graph precisely to those of the right graph, so that map defines an isomorphism of graphs.
The right graph has cycles of length $3$ (e.g., $aefa$) but he left graph does not, so the graphs cannot be isomorphic.