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pro vyhledávání: '"Damnjanovic, Ivan"'
A nut graph is a simple graph for which the adjacency matrix has a single zero eigenvalue such that all non-zero kernel eigenvectors have no zero entry. It is known that infinitely many $d$-regular nut graphs exist for $3 \leq d \leq 12$ and for $d \
Externí odkaz:
http://arxiv.org/abs/2410.14063
We present a universal and straightforward algebraic procedure for flat bands construction, polynomial indicator method. Using only Bloch Hamiltonian eigendeterminant functional to identify conditions that guarantee existence of nondispersive eigenva
Externí odkaz:
http://arxiv.org/abs/2410.09587
An expression is any mathematical formula that contains certain formal variables and operations to be executed in a specified order. In computer science, it is usually convenient to represent each expression in the form of an expression tree. Here, w
Externí odkaz:
http://arxiv.org/abs/2405.13928
Publikováno v:
Electron. J. Combin. 31 (2024) #P2.31
A nut graph is a simple graph whose adjacency matrix has the eigenvalue zero with multiplicity one such that its corresponding eigenvector has no zero entries. It is known that there exist no cubic circulant nut graphs. A bicirculant (resp. tricircul
Externí odkaz:
http://arxiv.org/abs/2312.14884
Autor:
Alizadeh, Yaser, Bašić, Nino, Damnjanović, Ivan, Došlić, Tomislav, Pisanski, Tomaž, Stevanović, Dragan, Xu, Kexiang
A nonnegative integer $p$ is realizable by a graph-theoretical invariant $I$ if there exist a graph $G$ such that $I(G) = p$. The inverse problem for $I$ consists of finding all nonnegative integers $p$ realizable by $I$. In this paper, we consider a
Externí odkaz:
http://arxiv.org/abs/2312.13083
Autor:
Damnjanović, Ivan
The transmission of a vertex in a connected graph is the sum of its distances to all the other vertices. A graph is transmission irregular (TI) when all of its vertices have mutually distinct transmissions. In an earlier paper, Al-Yakoob and Stevanov
Externí odkaz:
http://arxiv.org/abs/2311.14259
Autor:
Damnjanović, Ivan
A nut graph is a non-trivial simple graph such that its adjacency matrix has a one-dimensional null space spanned by a full vector. It was recently shown by the authors that there exists a $d$-regular circulant nut graph of order $n$ if and only if $
Externí odkaz:
http://arxiv.org/abs/2305.18658
Autor:
Damnjanović, Ivan
A circulant graph is a simple graph whose adjacency matrix can be represented in the form of a circulant matrix, while a nut graph is considered to be a graph whose null space is spanned by a single full vector. In a previous study by Damnjanovi\'c [
Externí odkaz:
http://arxiv.org/abs/2212.12959
Autor:
Damnjanović, Ivan, Ranđelović, Žarko
Publikováno v:
Filomat 38 (2024) 1085-1099
Among all trees on $n$ vertices with a given degree sequence, how do we maximise or minimise the sum over all adjacent pairs of vertices $x$ and $y$ of $f(\mathrm{deg} x, \mathrm{deg} y)$? Here $f$ is a fixed symmetric function satisfying a 'monotoni
Externí odkaz:
http://arxiv.org/abs/2212.03048
Autor:
Damnjanović, Ivan
A circulant nut graph is a non-trivial simple graph such that its adjacency matrix is a circulant matrix whose null space is spanned by a single vector without zero elements. Regarding these graphs, the order-degree existence problem can be thought o
Externí odkaz:
http://arxiv.org/abs/2212.03026