Iskanje po repozitoriju

Opis: In 2007, Miklavič and Potočnik proposed the problem of characterizing distance-regular Cayley graphs, which can be viewed as an extension of the problem of identifying strongly regular Cayley graphs, or equivalently, regular partial difference sets. Let p be an odd prime. In this paper, all distance-regular Cayley graphs over ℤps ⊕ ℤp are identified. It is shown that every such graph is isomorphic to a complete graph, a complete multipartite graph, or the line graph of a transversal design TD(r, p) with 2 ≤ r ≤ p − 1.
Ključne besede: distance-regular graph, Cayley graph, Schur ring, Fourier transformation, transversal design
Objavljeno v RUP: 21.10.2025; Ogledov: 342; Prenosov: 1
Celotno besedilo (461,23 KB)

Opis: A graph of order ▫$n$▫ is distance magic if it admits a bijective labeling of its vertices with integers from ▫$1$▫ to ▫$n$▫ such that each vertex has the same sum of the labels of its neighbors. This paper contributes to the long term project of characterizing all tetravalent distance magic graphs. With the help of a computer we find that out of almost nine million connected tetravalent graphs up to order 16 only nine are distance magic. In fact, besides the six well known wreath graphs there are only three other examples, one of each of the orders 12, 14 and 16. We introduce a generalization of wreath graphs, the so-called quasi wreath graphs, and classify all distance magic graphs among them. This way we obtain infinitely many new tetravalent distance magic graphs. Moreover, the two non-wreath graphs of orders 12 and 14 are quasi wreath graphs while the one of order 16 can be obtained from a quasi wreath graph of order 14 using a simple construction due to Kovář, Fronček and Kovářová.
Ključne besede: distance magic, tetravalent, quasi wreath graph
Objavljeno v RUP: 10.09.2025; Ogledov: 357; Prenosov: 5
Celotno besedilo (457,53 KB)

Ključne besede: graph distance, Wiener index, average distance, topological index, molecular descriptor, chemical graph theory
Objavljeno v RUP: 26.05.2025; Ogledov: 752; Prenosov: 7
Celotno besedilo (516,10 KB)

Ključne besede: distance-regularized vertex, pseudo-distance-regularized vertex, Terwilliger algebra, irreducible module, distance-balanced graph, nicely distance-balanced graph, strongly distance-balanced graph
Objavljeno v RUP: 15.02.2023; Ogledov: 3593; Prenosov: 116
Povezava na celotno besedilo

Opis: In this paper, a relation between graph distance matrices and Euclidean distance matrices (EDM) is considered. Graphs, for which the distance matrix is not an EDM (NEDM-graphs), are studied. All simple connected non-isomorphic graphs on ▫$n \le 8$▫ nodes are analysed and a characterization of the smallest NEDM-graphs, i.e., the minimal forbidden subgraphs, is given. It is proven that bipartite graphs and some subdivisions of the smallest NEDM-graphs are NEDM-graphs, too.
Ključne besede: graph theory, graph, Euclidean distance matrix, distance, eigenvalue
Objavljeno v RUP: 31.12.2021; Ogledov: 2332; Prenosov: 21
Celotno besedilo (711,65 KB)