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All Journal Electronic Journal of Graph Theory and Applications (EJGTA)
Mushtaq Shah
Department of Mathematics, AAAM Degree College, Bemina, Srinagar, India
Electrical & Electronics Engineering

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On 2-power unicyclic cubic graphs Shariefuddin Pirzada; Mushtaq Shah; Edy Tri Baskoro
Electronic Journal of Graph Theory and Applications (EJGTA) Vol 10, No 1 (2022): Electronic Journal of Graph Theory and Applications
Publisher : GTA Research Group, Univ. Newcastle, Indonesian Combinatorics Society and ITB

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.5614/ejgta.2022.10.1.24

Abstract

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.
Co-Authors Edy Tri Baskoro Shariefuddin Pirzada