Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: A near-polygonal graph is a graph Γ which has a set &#x1d49e; of m-cycles for some positive integer m such that each 2-path of Γ is contained in exactly one cycle in &#x1d49e;. If m is the girth of Γ then the graph is called polygonal. Given a polygonal graph Γ of valency r and girth m, Archdeacon and Perkel proved the existence of a polygonal graph Γ2 of valency r and girth 2m.  will show that this construction can be extended to one that yields a polygonal graph Γ3 of valency r and girth 3m, but that making the cycles any longer with this construction does not yield a polygonal graph.  also show that if Aut(Γ) is 2-arc transitive, so is Aut(Γk) for k = 2, 3. © 2010 Wiley Periodicals, Inc. J Graph Theory 68: 246-254, 2011 © 2011 Wiley Periodicals, Inc.
['Ákos Seress', 'Eric Swartz']
I am writing a research paper on a idea A note on the girth-doubling construction for polygonal graphs
[{"from": "human", "value": "I am writing a research paper on a idea A note on the girth-doubling construction for polygonal graphs"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: A near-polygonal graph is a graph \u0393 which has a set &#x1d49e; of m-cycles for some positive integer m such that each 2-path of \u0393 is contained in exactly one cycle in &#x1d49e;. If m is the girth of \u0393 then the graph is called polygonal. Given a polygonal graph \u0393 of valency r and girth m, Archdeacon and Perkel proved the existence of a polygonal graph \u03932 of valency r and girth 2m.  will show that this construction can be extended to one that yields a polygonal graph \u03933 of valency r and girth 3m, but that making the cycles any longer with this construction does not yield a polygonal graph.  also show that if Aut(\u0393) is 2-arc transitive, so is Aut(\u0393k) for k = 2, 3. \u00a9 2010 Wiley Periodicals, Inc. J Graph Theory 68: 246-254, 2011 \u00a9 2011 Wiley Periodicals, Inc."}]