Výsledky vyhľadávania
Názov Dual digraphs of finite meet-distributive and modular lattices Aut.údaje Andrew Craig ... [et al.] Autor Craig Andrew, P. K. (34%)
Spoluautori Haviar Miroslav 1965- (33%) UMBFP10 - Katedra matematiky
Marais Klarise (33%)
Zdroj.dok. Cubo : a mathematical journal. Vol. 26, no. 2 (2024), pp. 279-302. - Temuco : Department of mathematics and statistics of the Universidad de La Frontera, 2024 Kľúč.slová matematika - mathematics algebra - algebra teória zväzov geometria - geometry Form.deskr. články - journal articles Jazyk dok. angličtina Krajina Chile Anotácia We describe the digraphs that are dual representations of finite lattices satisfying conditions related to meet-distributivity and modularity. This is done using the dual digraph representation of finite lattices by Craig, Gouveia and Haviar (2015). These digraphs, known as TiRS digraphs, have their origins in the dual representations of lattices by Urquhart (1978) and Ploščica (1995). We describe two properties of finite lattices which are weakenings of (upper) semimodularity and lower semimodularity respectively, and then show how these properties have a simple description in the dual digraphs. Combined with previous work in this journal on dual digraphs of semidistributive lattices (2022), it leads to a dual representation of finite meet-distributive lattices. This provides a natural link to finite convex geometries. In addition, we present two sufficient conditions on a finite TiRS digraph for its dual lattice to be modular. We close by posing four open problems. URL Link na zdrojový dokument Kategória publikačnej činnosti ADE Číslo archívnej kópie 54691 Katal.org. BB301 - Univerzitná knižnica Univerzity Mateja Bela v Banskej Bystrici Báza dát xpca - PUBLIKAČNÁ ČINNOSŤ Odkazy PERIODIKÁ-Súborný záznam periodika Názov Cubo Podnázov a mathematical journal Vyd.údaje Temuco : Department of mathematics and statistics of the Universidad de La Frontera , 2024 ISSN 0716-7776 (print)0719-0646 (online) Form.deskr. časopisy - journals, elektronické časopisy - electronic journals Roč., číslo Vol. 26 no. 2 (2024) Jazyk dok. angličtina Krajina Chile URL Link na zdrojový dokument Kategória publikačnej činnosti GII Katal.org. BB301 - Univerzitná knižnica Univerzity Mateja Bela v Banskej Bystrici Báza dát xpca - PUBLIKAČNÁ ČINNOSŤ Odkazy - PERIODIKÁ - Súborný záznam periodika (1) - PUBLIKAČNÁ ČINNOSŤ Odkazy PERIODIKÁ-Súborný záznam periodika ČLÁNKY 2024: Dual digraphs of finite meet-distributive and modular lattices Názov Dual digraphs of finite semidistributive lattices Aut.údaje Andrew Craig ... [et al.] Autor Craig Andrew (34%)
Spoluautori Haviar Miroslav 1965- (33%) UMBFP10 - Katedra matematiky
São João José (33%)
Zdroj.dok. Cubo : a mathematical journal. Vol. 24, no. 3 (2022), pp. 369-392. - Temuco : Department of mathematics and statistics of the Universidad de La Frontera, 2021 Kľúč.slová grafové algoritmy algebraické štruktúry - algebraic structures matematika - mathematics Form.deskr. články - journal articles Jazyk dok. angličtina Krajina Chile Anotácia Dual digraphs of finite join-semidistributive lattices, meet-semidistributive lattices and semidistributive lattices are characterised. The vertices of the dual digraphs are maximal disjoint filter-ideal pairs of the lattice. The approach used here combines representations of arbitrary lattices due to Urquhart (1978) and Ploščcica (1995). The duals of finite lattices are mainly viewed as TiRS digraphs as they were presented and studied in Craig–Gouveia–Haviar (2015 and 2022). When appropriate, Urquhart’s two quasi-orders on the vertices of the dual digraph are also employed. Transitive vertices are introduced and their role in the domination theory of the digraphs is studied. In particular, finite lattices with the property that in their dual TiRS digraphs the transitive vertices form a dominating set (respectively, an in-dominating set) are characterised. A characterisation of both finite meet- and join-semidistributive lattices is provided via minimal closure systems on the set of vertices of their dual digraphs. URL Link na plný text Kategória publikačnej činnosti ADM Číslo archívnej kópie 52754 Katal.org. BB301 - Univerzitná knižnica Univerzity Mateja Bela v Banskej Bystrici Báza dát xpca - PUBLIKAČNÁ ČINNOSŤ Odkazy PERIODIKÁ-Súborný záznam periodika Názov Cubo Podnázov a mathematical journal Vyd.údaje Temuco : Department of mathematics and statistics of the Universidad de La Frontera , 2021 ISSN 0716-7776 (print)0719-0646 (online) Form.deskr. časopisy - journals, elektronické časopisy - electronic journals Roč., číslo Vol. 24 no. 3 (2022) Jazyk dok. angličtina Krajina Chile URL Link na zdrojový dokument Kategória publikačnej činnosti GII Katal.org. BB301 - Univerzitná knižnica Univerzity Mateja Bela v Banskej Bystrici Báza dát xpca - PUBLIKAČNÁ ČINNOSŤ Odkazy - PERIODIKÁ - Súborný záznam periodika (1) - PUBLIKAČNÁ ČINNOSŤ Odkazy PERIODIKÁ-Súborný záznam periodika ČLÁNKY 2022: Dual digraphs of finite semidistributive lattices Názov Cubo Podnázov a mathematical journal Vyd.údaje Temuco : Department of mathematics and statistics of the Universidad de La Frontera , 2021 ISSN 0716-7776 (print)0719-0646 (online) Form.deskr. časopisy - journals, elektronické časopisy - electronic journals Roč., číslo Vol. 23 no. 2 (2021) Jazyk dok. angličtina Krajina Chile URL Link na zdrojový dokument Kategória publikačnej činnosti GII Katal.org. BB301 - Univerzitná knižnica Univerzity Mateja Bela v Banskej Bystrici Báza dát xpca - PUBLIKAČNÁ ČINNOSŤ Odkazy - PERIODIKÁ - Súborný záznam periodika (1) - PUBLIKAČNÁ ČINNOSŤ Odkazy PERIODIKÁ-Súborný záznam periodika ČLÁNKY 2021: A new class of graceful graphs: k-enriched fan graphs and their characterisations Názov A new class of graceful graphs: k-enriched fan graphs and their characterisations Aut.údaje Miroslav Haviar, Samuel Kurtulík Autor Haviar Miroslav 1965- (50%) UMBFP10 - Katedra matematiky
Spoluautori Kurtulík Samuel (50%)
Zdroj.dok. 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 Kľúč.slová grafy - charts - graphs graciózne ohodnotenie grafov - graceful labelling of graphs grafové šachovnice - graph chessboards postupnosť Form.deskr. články - journal articles Jazyk dok. angličtina Krajina Chile Anotácia 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 Kategória publikačnej činnosti ADM Číslo archívnej kópie 50548 Katal.org. BB301 - Univerzitná knižnica Univerzity Mateja Bela v Banskej Bystrici Báza dát xpca - PUBLIKAČNÁ ČINNOSŤ Odkazy PERIODIKÁ-Súborný záznam periodika