On 2-power unicyclic cubic graphs

Shariefuddin Pirzada, Mushtaq Shah, Edy Tri Baskoro


In a graph, a cycle whose length is a power of two (that is, 2k) is called a 2-power cycle. In this paper, we show that the existence of an infinite family of cubic graphs which contain only one cycle whose length is a power of 2. Such graphs are called as 2-power unicyclic cubic graphs. Further we observe that the only 2-power cycle in a cubic graph cannot be removed implying that there does not exist a counter example for Erdos-Gyárfás conjecture.


cycle, cubic graph, Erdos-Gyarfas conjecture, distance

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DOI: http://dx.doi.org/10.5614/ejgta.2022.10.1.24


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