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Query: "author" (Vesna Iršič) .

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1.
Domination and independence numbers of large 2-crossing-critical graphs
Vesna Iršič, Maruša Lekše, Miha Pačnik, Petra Podlogar, Martin Praček, 2023, original scientific article

Abstract: After 2-crossing-critical graphs were characterized in 2016, their most general subfamily, large 3-connected 2-crossing-critical graphs, has attracted separate attention. This paper presents sharp upper and lower bounds for their domination and independence number.
Keywords: crossing-critical graphs, domination number, independence number
Published in DiRROS: 09.04.2024; Views: 60; Downloads: 34
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2.
Generalized Pell graphs
Vesna Iršič, Sandi Klavžar, Elif Tan, 2023, original scientific article

Abstract: In this paper, generalized Pell graphs $\Pi_{n,k}$, $k\ge 2$, are introduced. The special case of $k=2$ are the Pell graphs $\Pi_{n}$ defined earlier by Munarini. Several metric, enumerative, and structural properties of these graphs are established. The generating function of the number of edges of $\Pi_{n,k}$ and the generating function of its cube polynomial are determined. The center of $\Pi_{n,k}$ is explicitly described; if $k$ is even, then it induces the Fibonacci cube $\Gamma_{n}$. It is also shown that $\Pi_{n,k}$ is a median graph, and that $\Pi_{n,k}$ embeds into a Fibonacci cube.
Keywords: Fibonacci cubes, Pell graphs, generating functions, center of graph, median graphs, k-Fibonacci sequence
Published in DiRROS: 08.04.2024; Views: 83; Downloads: 35
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3.
General position polynomials
Vesna Iršič, Sandi Klavžar, Gregor Rus, James Tuite, 2024, original scientific article

Abstract: A subset of vertices of a graph $G$ is a general position set if no triple of vertices from the set lie on a common shortest path in $G$. In this paper we introduce the general position polynomial as $\sum_{i \geq 0} a_i x^i$, where $a_i$ is the number of distinct general position sets of $G$ with cardinality $i$. The polynomial is considered for several well-known classes of graphs and graph operations. It is shown that the polynomial is not unimodal in general, not even on trees. On the other hand, several classes of graphs, including Kneser graphs $K(n,2)$, with unimodal general position polynomials are presented.
Keywords: general position set, general position number, general position polynomial, unimodality, trees, Cartesian product of graphs, Kneser graphs
Published in DiRROS: 28.02.2024; Views: 118; Downloads: 80
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