D Stevanovi's research while affiliated with University of Niš and other places
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Publications (6)
In this note, we present an apparently new and rather short proof of a celebrated theorem of Horst Sachs characterizing bipartite nite graphs in term of their eigenvalue spectrum. Moreover, the simplicity of the proof allows us to establish this theorem and related results as a special instance of much more general assertions regarding the spectral...
Recently, Berman and Zhang (Discrete Math. 260 (2003) 27) obtained an upper bound for the bipartite density of cubic graphs in terms of the smallest eigenvalue of an adjacency matrix and attempted to characterize graphs for which the upper bound is attained. Here we do characterize graphs for which the upper bound is attained, and correct a few err...
We determine all connected 4-regular integral graphs avoiding ±3 in the spectrum. There are exactly 16 bipartite and 8 nonbipartite such graphs. The smallest bipartite one is K4,4, while the largest has 32 vertices. Among these graphs there are two triplets of cospectral nonisomorphic graphs and two pairs of cospectral nonisomorphic graphs. The sma...
A graph whose spectrum consists entirely of integers is called an integral graph. We present a survey of results on integral graphs and on the corre-sponding proof techniques. Throughout this paper a graph G is assumed to be simple, i.e. a finite undi-rected graph without loops or multiple edges. Therefore, the characteristic polyno-mial of (the ad...
Possible spectra of 4-regular integral graphs are determined. Some constructions and a list of 65 known connected 4-regular integral graphs are given.
Using graph angles and previous results from [8] we show that a connected bipar-tite 4-regular integral graph has at most 1260 vertices, except if it has one of five exceptional spectra.
Citations
... In 1998, D. Cvetković, S. Simić, and D. Stevanović [5] found 1888 possible spectra of 4-regular bipartite integral graphs, more than 500 of which does not exist as it was shown in [15]. They also published a list of 65 known 4regular connected integral graphs. ...
... • 65 four-regular integral graphs of order n ¥ 90 by the use of graph operations [8] and all these graphs of order n < 20 [22], ...
... In this article, we first discuss the concept of integrability in graphs, a problem initially posed by Harary and Schwenk in [10]. Various articles have emerged on this interesting area of research, discussing integral graphs associated with different matrices like adjacency [2] and Laplacian matrices [16]. Note that every threshold graph is integral for the Laplacian matrix [16]. ...
... Radosavljevi´c and Simi´c in [19] determined all thirteen nonregular nonbipartite connected integral graphs with maximum degree four. Stevanovi´c [22] determined all connected 4-regular integral graphs avoiding ±3 in the spectrum. A survey of results on integral graphs may be found in [6]. ...
