Cycle multiplicity of a graph G is the maximum number of edge disjoint cycles in G. In this paper, we determine the
cycle multiplicity of and then obtain the formula of cycle
multiplicity of total graph of complete bipartite graph, this generalizes the
result for, which is given by M.M.
Akbar Ali in [1].
References
[1]
Akbar Ali, M.M. and Panayappan, S. (2010) Cycle Multiplicity of Total Graph of Cn, Pn, and K1,n. International Journal of Engineering, Science and Technology, 2, 54-58. https://doi.org/10.4314/ijest.v2i2.59138
[2]
Chatrand, G., Geller, D. and Hedetniemi, S. (1971) Graphs with Forbidden Subgraphs. Journal of Combinatorial Theory, 10, 12-41. https://doi.org/10.1016/0095-8956(71)90065-7
[3]
Simoes Pereira, J.M.S. (1972) A Note of Cycle Multiplicity of Line Graphs and Total Graphs. Journal of Combinatorial Theory, 12, 194-200. https://doi.org/10.1016/0095-8956(72)90024-X
[4]
Li, Y.K. (2017) Cycle Multiplicity of Some Total Graphs. Applied Mathematics and Computation, 292, 107-113. https://doi.org/10.1016/j.amc.2016.06.042
[5]
Song, C.J., Wang, Y. and Yan, J. (2023) Disjoint Cycles and Degree Sum Condition in a Graph. Journal of the Operations Research Society of China, 1-16. https://doi.org/10.1007/s40305-023-00473-5
[6]
Bondy, J.A. and Murty, U.S.R. (1976) Graph Theory with Applications. Macmillan, London.
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