1. Classification of pentavalent symmetric tricirculantsYasamin Khaefi, Klavdija Kutnar, Dragan Marušič, 2026, izvirni znanstveni članek Opis: A graph $\Gamma$ is said to be an {\em $m$-Cayley graph} on a group $G$ ($|G|\ne 1$) if its automorphism group contains a semiregular subgroup isomorphic to $G$ having $m$ orbits on the vertex set of $\Gamma$. If $G$ is cyclic and $m=3$ then $\Gamma$ is called a {\em tricirculant}. A graph is said to be {\em symmetric} if its automorphism group acts transitively on the set of its arcs. In this paper, it is shown that with the exception of $K_6$, no connected pentavalent symmetric tricirculant exists.
Ključne besede: pentavalent graph, symmetric, semiregular automorphism, tricirculant
Objavljeno v RUP: 22.06.2026; Ogledov: 254; Prenosov: 9
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2. Homomorphisms from the Coxeter graphMarko Orel, Draženka Višnjić, 2025, izvirni znanstveni članek Opis: Let $S_n(\mathbb{F}_2)$ be the set of all $n\times n$ symmetric matrices with coefficients in the binary field $\mathbb{F}_2=\{0,1\}$, and let $SGL_n(\mathbb{F}_2)$ be its subset formed by invertible matrices. Let $\widehat{\Gamma}_n$ be the graph with the vertex set $S_n(\mathbb{F}_2)$ where a pair of vertices $\{A,B\}$ form an edge if and only if $rank(A-B)=1$. Similarly, let $\Gamma_n$ be the subgraph in $\widehat{\Gamma}_n$, which is induced by the set $SGL_n(\mathbb{F}_2)$. Graph $\Gamma_n$ generalizes the well-known Coxeter graph, which is isomorphic to $\Gamma_3$. Motivated by research topics in coding theory, matrix theory, and graph theory, this paper represents the first step towards the characterization of all graph homomorphisms $\Phi: \Gamma_n\to \widehat{\Gamma}_m$ where $n,m$ are positive integers. Here, the case $n=3$ is solved.
Ključne besede: preserver problems, symmetric matrices, invertible matrices, binary field, rank, graph homomorphisms, Coxeter graph
Objavljeno v RUP: 27.08.2025; Ogledov: 908; Prenosov: 5
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3. The distance function on Coxeter-like graphs and self-dual codesMarko Orel, Draženka Višnjić, 2025, izvirni znanstveni članek Ključne besede: Coxeter graph, invertible symmetric matrices, binary field, rank, distance in graphs, alternate matrices, self-dual codes
Objavljeno v RUP: 30.05.2025; Ogledov: 1262; Prenosov: 21
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6. Odd extensions of transitive groups via symmetric graphs - The cubic caseKlavdija Kutnar, Dragan Marušič, 2018, izvirni znanstveni članek Opis: When dealing with symmetry properties of mathematical objects, one of the fundamental questions is to determine their full automorphism group. In this paper this question is considered in the context of even/odd permutations dichotomy. More precisely: when is it that the existence of automorphisms acting as even permutations on the vertex set of a graph, called even automorphisms, forces the existence of automorphisms that act as odd permutations, called odd automorphisms. As a first step towards resolving the above question, complete information on the existence of odd automorphisms in cubic symmetric graphs is given.
Ključne besede: automorphism group, arc-transitive, even permutation, odd permutation, cubic symmetric graph
Objavljeno v RUP: 19.11.2018; Ogledov: 4421; Prenosov: 213
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9. Cubic symmetric graphs via odd automorphisms, 60th Birthday Lecture Series, Department of Mathematics, University of Auckland, New Zealand, 10 September 2015Klavdija Kutnar, 2015, predavanje na tuji univerzi Ključne besede: cubic graph, symmetric, automorphism, odd permutation
Objavljeno v RUP: 15.10.2015; Ogledov: 4294; Prenosov: 31
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