On 2-power unicyclic cubic graphs - Shariefuddin Pirzada; Mushtaq Shah; Edy Tri Baskoro (GTA Research Group, Univ. Newcastle, Indonesian Combinatorics Society and ITB, 2022)
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.