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Title A survey on chessboard representations of classes of graceful graphs Author info Miroslav Haviar, Michal Ivaška Author Haviar Miroslav 1965- (50%) UMBFP10 - Katedra matematiky
Co-authors Ivaška Michal 1987- (50%)
Source document Acta Universitatis Matthiae Belii : series Mathematics, Vol. 29. Pp. 1-38. - Banská Bystrica : Vydavateľstvo Univerzity Mateja Bela - Belianum, 2021 Keywords grafy - charts - graphs graciózne ohodnotenie grafov - graceful labelling of graphs postupnosť Form. Descr. články - journal articles Language English Country Slovak Republic Annotation This is a survey on chessboard representations of classes of graceful graphs. We introduced and studied the concept of chessboard representations of graceful graphs in our book Vertex labellings of simple graphs in 2015, however, the book and hence its concepts and methods are not widely accessible. Our survey from the book is complemented by new applications of chessboard representations to the classes of k-enriched fan graphs presented by the first author and Kurtulík in 2021. The aim of the chessboard representations of classes of graceful graphs has been to provide an important value of visualization. Firstly, it leads to seeing better the pattern of the graceful labellings in already known graceful representations of simple graphs. Secondly, it can lead to creating new classes of graceful graphs as is demonstrated on the very recent example of the classes of k-enriched fan graphs. URL Link na plný text Public work category AED No. of Archival Copy 51542 Catal.org. BB301 - Univerzitná knižnica Univerzity Mateja Bela v Banskej Bystrici Database xpca - PUBLIKAČNÁ ČINNOSŤ Title A new class of graceful graphs: k-enriched fan graphs and their characterisations Author info Miroslav Haviar, Samuel Kurtulík Author Haviar Miroslav 1965- (50%) UMBFP10 - Katedra matematiky
Co-authors Kurtulík Samuel (50%)
Source document Cubo : a mathematical journal. Vol. 23, č. 2 (2021), pp. 313-331. - Temuco : Department of mathematics and statistics of the Universidad de La Frontera, 2021 Keywords grafy - charts - graphs graciózne ohodnotenie grafov - graceful labelling of graphs grafové šachovnice - graph chessboards postupnosť Form. Descr. články - journal articles Language English Country Chile Annotation The Graceful Tree Conjecture stated by Rosa in the mid 1960s says that every tree can be gracefully labelled. It is one of the best known open problems in Graph Theory. The conjecture has caused a great interest in the study of gracefulness of simple graphs and has led to many new contributions to the list of graceful graphs. However, it has to be acknowledged that not much is known about the structure of graceful graphs after 55 years. Our paper adds an infinite family of classes of graceful graphs to the list of known simple graceful graphs. We introduce classes of k-enriched fan graphs kF_n for all integers k, n ≥ 2 and we prove that these graphs are graceful. Moreover, we provide characterizations of the k-enriched fan graphs kF_n among all simple graphs via Sheppard's labelling sequences introduced in the 1970s, as well as via labelling relations and graph chessboards. These last approaches are new tools for the study of graceful graphs introduced by Haviar and Ivaška in 2015. The labelling relations are closely related to Sheppard's labelling sequences while the graph chessboards provide a nice visualization of graceful labellings. We close our paper with an open problem concerning another infinite family of extended fan graphs. URL Link na zdrojový dokument Link na plný text Public work category ADM No. of Archival Copy 50548 Catal.org. BB301 - Univerzitná knižnica Univerzity Mateja Bela v Banskej Bystrici Database xpca - PUBLIKAČNÁ ČINNOSŤ References PERIODIKÁ-Súborný záznam periodika Title Štruktúra a vývojová dynamika lesných ekosystémov s borovicou limbovou (Pinus Cembra L.) pod hornou hranicou lesa vo Vysokých Tatrách Author info Ivan Vološčuk Author Vološčuk Ivan 1935- (100%) UMBFP11 - Inštitút výskumu krajiny a regiónov
Source document Lesnícky časopis : vedecký štvrťročník pre všetky oblasti lesníckeho výskumu : scientific quarterly for all aspects of forestry research. Roč. 58, č. 4 (2012), s. 243-256. - Zvolen : Národné lesnícke centrum, 2012 Keywords štruktúra lesa postupnosť etapy vývoja forest structure ekologická sukcesia - ecological succession developmental stages Language Slovak Country Slovak Republic systematics 630 Public work category ADF No. of Archival Copy 26897 Catal.org. BB301 - Univerzitná knižnica Univerzity Mateja Bela v Banskej Bystrici Database xpca - PUBLIKAČNÁ ČINNOSŤ References PERIODIKÁ-Súborný záznam periodika Title Postupnosti a nekonečné rady pre učiteľov Par.title Sequences and infinite series for teachers Author info Katarína Čunderlíková; rec. Vladimír Janiš, Martin Kalina Author Čunderlíková Katarína 1994- (100%) UMBFP10 - Katedra matematiky
Another authors Janiš Vladimír 1963- (Recenzent)
Kalina Martin (Recenzent)
Issue data Banská Bystrica : Univerzita Mateja Bela, Fakulta prírodných vied , 2011. - 108 s. Issue 1. vyd. ISBN 978-80-557-0273-5 Keywords postupnosť vlastnosti postupnosti aritmetická postupnosť postupnosti - sequences properties of seguence Language Slovak Country Slovak Republic systematics 5 Public work category BCI No. of Archival Copy 20936 Catal.org. BB301 - Univerzitná knižnica Univerzity Mateja Bela v Banskej Bystrici Database xpca - PUBLIKAČNÁ ČINNOSŤ Title On topological dynamics of sequences of continuous maps Author info Sergii Kolyada, Ľubomír Snoha Title Subtitle Translation : O topologickej dynamike postupností spojitých zobrazení Author Kolyada Sergiy
Co-authors Snoha Ľubomír 1955- UMBFP10 - Katedra matematiky
Action Conference 30-Years After Sharkovskiis Theorem - New Perspectives . konferencia , Murcia , 13.-18.06.1994 Source document International Journal of Bifurcation and Chaos : in Applied Sciences and Engineering. Vol. 5, no. 5 (1995), pp. 1437-1438. - Singapore : World Scientific Publishing, 1995 Keywords topologická entropia - topological entropy zobrazenia spojité postupnosť štúdie Language English systematics 515.1 Public work category AFC Repercussion category MURILLO-ARCILA, M. - PERIS, A. Mixing properties for nonautonomous linear dynamics and invariant sets. In Applied mathematics letters. ISSN 0893-9659, 2013, vol. 26, no. 2, pp. 215-218.
CANOVAS, J. S. On omega-limit sets of non-autonomous discrete systems. In Journal of difference equations and applications. ISSN 1023-6198, 2006, vol. 12, no. 1, pp. 95-100.
CANOVAS, Jose S. - PUU, Toenu - MARIN, Manuel Ruiz. A method for studying non-autonomous affine maps: An application to a two-region business cycle model. In Chaos solitons & fractals. ISSN 0960-0779, 2007, vol. 34, no. 4, pp. 1285-1298.
DVORAKOVA, Jana - NEUMAERKER, Natascha - STEFANKOVA, Marta. On omega-limit sets of non-autonomous dynamical systems with a uniform limit of type 2(infinity). In Journal of difference equations applications. ISSN 1023-6198, 2016, vol. 22, no. 4, pp. 636-644.
Catal.org. UKUMB###UK UMB###BB301 - Univerzitná knižnica Univerzity Mateja Bela v Banskej Bystrici Database xpca - PUBLIKAČNÁ ČINNOSŤ References PERIODIKÁ-Súborný záznam periodika