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
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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