### On 2-power unicyclic cubic graphs

#### Abstract

In a graph, a cycle whose length is a power of two (that is, 2^{k}) 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.

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

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