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The relationships between eigenvalues and eigenvectors of a product graph and those of its factor graphs have been known for the standard products, while characterization of Laplacian eigenvalues and eigenvectors of the Kronecker product of graphs us
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::c9296232571074dd729d2aa546c11b7e
Publikováno v:
Fuzzy Sets and Systems. 333:124-139
In this paper we consider different types of ranks of fuzzy matrices over residuated lattices. We investigate relations between ranks and prove that row rank, column rank and Schein rank of idempotent fuzzy matrices are equal. In particular, ranks an
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https://explore.openaire.eu/search/publication?articleId=doi_________::82c2de9673cea4ced46610a33027a010
https://doi.org/10.1016/j.fss.2017.05.028
https://doi.org/10.1016/j.fss.2017.05.028
Autor:
Milan Bašić
Publikováno v:
Filomat. 32:71-85
Classes of circulant graphs play an important role in modeling interconnection networks in parallel and distributed computing. They also find applications in modeling quantum spin networks supporting the perfect state transfer. It has been noticed th
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::743dc8416ae43b3035af2807755fa9f4
https://doi.org/10.2298/fil1801071b
https://doi.org/10.2298/fil1801071b
Publikováno v:
Algebraic Informatics ISBN: 9783030213626
CAI
CAI
Integral circulant graphs are proposed as models for quantum spin networks. Specifically, it is important to know how far information can potentially be transferred between nodes of the quantum networks modeled by integral circulant graphs and this t
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https://explore.openaire.eu/search/publication?articleId=doi_________::ed8163ec6b5dd3f5f167a170bc34c830
https://doi.org/10.1007/978-3-030-21363-3_7
https://doi.org/10.1007/978-3-030-21363-3_7
Autor:
Aleksandar Ilic, Milan Bašić
Given a graph $G$, we associate a path matrix $P$ whose $(i, j)$ entry represents the maximum number of vertex disjoint paths between the vertices $i$ and $j$, with zeros on the main diagonal. In this note, we resolve four conjectures from [M. M. Shi
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::0046f1849eb5246a04dab79ae61e1a91
Autor:
Aleksandar Ilic, Milan Bašić
Publikováno v:
Filomat. 29:2079-2086
The unitary Cayley graph Xn has the vertex set Zn = {0,1,2,..., n-1} and vertices a and b are adjacent, if and only if gcd(a-b,n) = 1. In this paper, we present some properties of the clique, independence and distance polynomials of the unitary Cayle
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::6e375091dc86b06996508ef98dc84791
https://doi.org/10.2298/fil1509079b
https://doi.org/10.2298/fil1509079b
Autor:
Milan Bašić
Publikováno v:
Quantum Information Processing. 12:345-364
In this paper we answer the question of when circulant quantum spin networks with nearest-neighbor couplings can give perfect state transfer. The network is described by a circulant graph G, which is characterized by its circulant adjacency matrix A.
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::8a950bf7b4064c919aceb3df501010a5
https://doi.org/10.1007/s11128-012-0381-z
https://doi.org/10.1007/s11128-012-0381-z
Autor:
Milan Bašić, Marko D. Petković
Publikováno v:
Computers & Mathematics with Applications. 61:300-312
For a given graph G, denote by A its adjacency matrix and F(t)=exp(iAt). We say that there exist a perfect state transfer (PST) in G if |F(@t)"a"b|=1, for some vertices a,b and a positive real number @t. Such a property is very important for the mode
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https://explore.openaire.eu/search/publication?articleId=doi_________::82059d11ad3faecc3915b5d6e370a12c
https://doi.org/10.1016/j.camwa.2010.11.005
https://doi.org/10.1016/j.camwa.2010.11.005
Autor:
Aleksandar Ilic, Milan Bašić
Publikováno v:
Computers & Mathematics with Applications. 60(1):144-150
Integral circulant graphs are a generalization of unitary Cayley graphs, recently studied by Klotz and Sander. The integral circulant graph Xn(D) has vertices 0,1,…,n−1, and two vertices a and b are adjacent iff gcd(x−y,n)∈D, where D⊆{d:d
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::643851b9ff3c04f1c40c5c7444ce5e8a