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95. On the metric subgraphs of a graphYanan Hu, Xingzhi Zhan, 2025, izvirni znanstveni članek Opis: The three subgraphs of a connected graph induced by the center, annulus and periphery are called its metric subgraphs. The main results are as follows. (1) There exists a graph of order n whose metric subgraphs are all paths if and only if n ≥ 13 and the smallest size of such a graph of order 13 is 22; (2) there exists a graph of order n whose metric subgraphs are all cycles if and only if n ≥ 15, and there are exactly three such graphs of order 15; (3) for every integer k ≥ 3, we determine the possible orders for the existence of a graph whose metric subgraphs are all connected k-regular graphs; (4) there exists a graph of order n whose metric subgraphs are connected and pairwise isomorphic if and only if n ≥ 24 and n is divisible by 3. An unsolved problem is posed.
Ključne besede: center, annulus, periphery, metric subgraphs, path, cycle
Objavljeno v RUP: 16.09.2025; Ogledov: 315; Prenosov: 5
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96. Answers to questions about medial layer graphs of self-dual regular and chiral polytopesMarston Conder, Isabelle Steinmann, 2025, izvirni znanstveni članek Opis: An abstract n-polytope P is a partially-ordered set which captures important properties of a geometric polytope, for any dimension n. For even n ≥ 2, the incidences between elements in the middle two layers of the Hasse diagram of P give rise to the medial layer graph of P, denoted by G = G(P). If n = 4, and P is both highly symmetric and self-dual of type {p, q, p}, then a Cayley graph C covering G can be constructed on a group of polarities of P. In this paper we address some open questions about the relationship between G and C that were raised in a 2008 paper by Monson and Weiss, and describe some interesting examples of these graphs. In particular, we give the first known examples of improperly self-dual chiral polytopes of type {3, q, 3}, which are also among the very few known examples of highly symmetric self-dual finite polytopes that do not admit a polarity. Also we show that if p = 3 then C cannot have a higher degree of s-arc-transitivity than G, and we present a family of regular 4-polytopes of type {6, q, 6} for which the vertex-stabilisers in the automorphism group of C are larger than those for G.
Ključne besede: abstract polytope, regular polytope, chiral polytope, medial graph
Objavljeno v RUP: 16.09.2025; Ogledov: 336; Prenosov: 11
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97. Growth, morphology and reproductive phenology of Gelidium adriaticum (Gelidiales, Rhodophyta) from the Slovenian coast (Gulf of Trieste, northern Adriatic)Claudio Battelli, Peter Glasnović, 2025, izvirni znanstveni članek Opis: The occurrence, growth, external morphology and reproductive phenology of a Gelidium adriaticum settlement from the midlittoral zone in St. Simon Bay (Slovenian coast, Gulf of Trieste, northern Adriatic Sea) were investigated. The study was based on monthly sampling conducted for one year, from January to December 2023. The studied settlement was well developed in shaded rock crevices, forming dense turfs with a very patchy and irregular distribution. It was character-ized by a slight predominance of tetrasporic thalli, with a ratio between the three reproductive stages (tetrasporic:sterile:cystocarpic) of 1.19:1.04:1.00. The mean values of the morphological characteristics studied (height and width of the thallus, width of the widest part of the thallus axis, width of the apical, middle and basal parts of the erect axes) varied between seasons and reproductive stages. In general, these values were lower in the cystocarpic thalli than those in the tetrasporic and sterile stages in all seasons.
Ključne besede: Gelidium adriaticum, midlittoral, growth, morphology, reproductive phenology, Slovenian coast, northern Adriatic
Objavljeno v RUP: 15.09.2025; Ogledov: 383; Prenosov: 4
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