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Journal of Combinatorial Mathematics and Combinatorial Computing

  • Research article

The spectrum problem for two multigraphs with four vertices and seven edges

H. Bermudez1, R. C. Bunge2, E. D. Cornelius2, S. I. El-Zanati2, W. H. Mamboleo3, N. T. Nguyen2, D. P. Roberts4
1University of Puerto Rico Mayaguez Campus, Mayaguez, PR 00682
2Campus Box 4520, Illinois State University, Normal, IL 61790
3North Carolina State University, Raleigh, NC 27695
4Illinois Wesleyan University, Bloomington, IL 61701

Abstract

Let \( G \) be one of the two multigraphs obtained from \( K_4-e \) by replacing two edges with a double-edge while maintaining a minimum degree of 2. We find necessary and sufficient conditions on \( n \) and \(\lambda\) for the existence of a \( G \)-decomposition of \( K_n \).

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Citation
H. Bermudez, R. C. Bunge, E. D. Cornelius, S. I. El-Zanati, W. H. Mamboleo, N. T. Nguyen, D. P. Roberts. The spectrum problem for two multigraphs with four vertices and seven edges[J], Journal of Combinatorial Mathematics and Combinatorial Computing, Volume 114. 31-45. .