| Authors: | De Abreu, Nair Balińska, Krystyna Simić, Slobodan Zwierzyński, Krzysztof |
Title: | More on non-regular bipartite integral graphs with maximum degree 4 not having ±1 as eigenvalues | Journal: | Applicable Analysis and Discrete Mathematics | Volume: | 8 | Issue: | 1 | First page: | 123 | Last page: | 154 | Issue Date: | 1-Mar-2014 | Rank: | M21 | ISSN: | 1452-8630 | DOI: | 10.2298/AADM140228004A | Abstract: | A graph is integral if the spectrum (of its adjacency matrix) consists entirely of integers. The problem of determining all non-regular bipartite integral graphs with maximum degree four which do not have ±1 as eigenvalues was posed in K.T. Balińska, S.K. Simić, K.T. Zwierzyński: Which nonregular bipartite integral graphs with maximum degree four do not have ±1 as eigenvalues? DiscreteMath., 286 (2004), 15-25. Here we revisit this problem, and provide its complete solution using mostly the theoretical arguments. |
Keywords: | Adjacency matrix | Graph spectrum | Integral graph | Publisher: | School of Electrical Engineering, University of Belgrade | Project: | CNDq, Brazil, Grant 300563/94(NV) Graph theory and mathematical programming with applications in chemistry and computer science Development of new information and communication technologies, based on advanced mathematical methods, with applications in medicine, telecommunications, power systems, protection of national heritage and education Poznan University of Technology, Grant DS 4-45-105/13 |
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