# On the metamorphosis of a G-design into a (G - e) -design

Sutton, Matthew William (2014) On the metamorphosis of a G-design into a (G - e) -design. Discrete Mathematics, 318 1: 71-77. doi:10.1016/j.disc.2013.11.014

Author Sutton, Matthew William On the metamorphosis of a G-design into a (G - e) -design On the metamorphosis of a G-design into a (G - e) -design Discrete Mathematics   Check publisher's open access policy 0012-365X1872-681X 2014-03-01 2013 Article (original research) 10.1016/j.disc.2013.11.014 Not yet assessed 318 1 71 77 7 Amsterdam, Netherlands Elsevier eng 2607 Discrete Mathematics and Combinatorics2614 Theoretical Computer Science A G-design of order v is an edge disjoint decomposition of into copies of the graph G. A metamorphosis of a G-design of order v into a (G-e)-design of order v is obtained by retaining the graph G-e from each block of G in the design, and rearranging the remaining edges to form further copies of G-e. Here, we prove that if a graph G with n edges admits an α-labelling and the graph G-e admits a -labelling, then there is a metamorphosis of a G-design of order 2n(n-1)x+1 into a (G-e)-design of the same order for all integers x. A G-design of order v is an edge disjoint decomposition of Kv into copies of the graph G. A metamorphosis of a G-design of order v into a (G – e)-design of order v is obtained by retaining the graph G – e from each block of G in the design, and rearranging the remaining edges to form further copies of G – e. Here, we prove that if a graph G with n edges admits an α-labelling and the graph G – e admits a ρ+-labelling, then there is a metamorphosis of a G-design of order 2n(n-1)x+1 into a (G – e)-design of the same order for all integers x. Cyclic graph decompositionLabellings of graphsMetamorphosis C1 Confirmed Code UQ

 Document type: Journal Article Article (original research) School of Mathematics and Physics Official 2014 Collection

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