More on non-regular bipartite integral graphs with maximum degree 4 not having ±1 as eigenvalues

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. Bali?ska, S.K. Simic, K.T. Zwierzy?ski: Which non-regular bipartite integral graphs with maximum degree four do not have ?1 as eigenvalues?, Discrete Math., 286 (2004), 15{25. Here we revisit this problem, and provide its complete solution using mostly the theoretical arguments.