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21.
On the recognition of k-equistable graphs
Vadim E. Levit, Martin Milanič, D. Tankus, 2012, objavljeni znanstveni prispevek na konferenci

Najdeno v: ključnih besedah
Povzetek najdenega: ...maximal stable set, equistable graph, polynomial time algorithm, ...
Ključne besede: maximal stable set, equistable graph, polynomial time algorithm
Objavljeno: 15.10.2013; Ogledov: 1243; Prenosov: 61
URL Polno besedilo (0,00 KB)

22.
Leonard triples and hypercubes
Štefko Miklavič, 2007, izvirni znanstveni članek

Opis: Let ▫$V$▫ denote a vector space over ▫$\mathbb{C}$▫ with finite positive dimension. By a Leonard triple on ▫$V$▫ we mean an ordered triple of linear operators on ▫$V$▫ such that for each of these operators there exists a basis of ▫$V$▫ with respect to which the matrix representing that operator is diagonal and the matrices representing the other two operators are irreducible tridiagonal. Let ▫$D$▫ denote a positive integer and let ▫${\mathcal{Q}}_D$▫ denote the graph of the ▫$D$▫-dimensional hypercube. Let ▫$X$ denote the vertex set of ▫${\mathcal{Q}}_D$▫ and let ▫$A \in {\mathrm{Mat}}_X ({\mathbb{C}})$▫ denote the adjacency matrix of ▫${\mathcal{Q}}_D$▫. Fix ▫$x \in X$▫ and let ▫$A^\ast \in {\mathrm{Mat}}_X({\mathbb{C}})$▫ denote the corresponding dual adjacency matrix. Let ▫$T$▫ denote the subalgebra of ▫${\mathrm{Mat}}_X({\mathbb{C}})$ generated by ▫$A,A^\ast$▫. We refer to ▫$T$▫ as the Terwilliger algebra of ▫${\mathcal{Q}}_D$▫ with respect to ▫$x$▫. The matrices ▫$A$▫ and ▫$A^\ast$▫ are related by the fact that ▫$2iA = A^\ast A^\varepsilon - A^\varepsilon A^\ast$▫ and ▫$2iA^\ast = A^\varepsilon A - AA^\varepsilon$▫, where ▫$2iA^\varepsilon = AA^\ast - A^\ast A$▫ and ▫$i^2 = -1$▫. We show that the triple ▫$A$▫, ▫$A^\ast$▫, ▫$A^\varepsilon$▫ acts on each irreducible ▫$T$▫-module as a Leonard triple. We give a detailed description of these Leonard triples.
Najdeno v: ključnih besedah
Povzetek najdenega: ...positive integer and let ▫${\mathcal{Q}}_D$▫ denote the graph of the ▫$D$▫-dimensional hypercube. Let ▫$X$ denote...
Ključne besede: mathematics, graph theory, Leonard triple, distance-regular graph, hypercube, Terwilliger algebra
Objavljeno: 15.10.2013; Ogledov: 1558; Prenosov: 60
URL Polno besedilo (0,00 KB)

23.
On the connectivity of bipartite distance-balanced graphs
Štefko Miklavič, Primož Šparl, 2012, izvirni znanstveni članek

Opis: A connected graph ▫$\varGamma$▫ is said to be distance-balanced whenever for any pair of adjacent vertices ▫$u,v$▫ of ▫$\varGamma$▫ the number of vertices closer to ▫$u$▫ than to ▫$v$▫ is equal to the number of vertices closer to ▫$v$▫ than to ▫$u$▫. In [K. Handa, Bipartite graphs with balanced ▫$(a,b)$▫-partitions, Ars Combin. 51 (1999), 113-119] Handa asked whether every bipartite distance-balanced graph, that is not a cycle, is 3-connected. In this paper the Handa question is answered in the negative. Moreover, we show that a minimal bipartite distance-balanced graph, that is not a cycle and is not 3-connected, has 18 vertices and is unique. In addition, we give a complete classification of non-3-connected bipartite distance-balanced graphs for which the minimal distance between two vertices in a 2-cut is three. All such graphs are regular and for each ▫$k \geq 3$▫ there exists an infinite family of such graphs which are ▫$k$▫-regular.Furthermore, we determine a number of structural properties that a bipartite distance-balanced graph, which is not 3-connected, must have. As an application, we give a positive answer to the Handa question for the subfamily of bipartite strongly distance-balanced graphs.
Najdeno v: ključnih besedah
Povzetek najdenega: ...A connected graph ▫$\varGamma$▫ is said to be distance-balanced whenever...
Ključne besede: graph theory, connected graphs, connectivity, distance-balanced graphs, bipartite graphs
Objavljeno: 15.10.2013; Ogledov: 1345; Prenosov: 49
URL Polno besedilo (0,00 KB)

24.
The full automorphism group of a Cayley graph
Gabriel Verret, 2013, objavljeni povzetek znanstvenega prispevka na konferenci (vabljeno predavanje)

Najdeno v: ključnih besedah
Ključne besede: automorphism group, Cayley graph
Objavljeno: 15.10.2013; Ogledov: 2293; Prenosov: 20
URL Polno besedilo (0,00 KB)
Gradivo ima več datotek! Več...

25.
Large sets of long distance equienergetic graphs
Dragan Stevanović, 2009, izvirni znanstveni članek

Opis: Distance energy of a graph is a recent energy-type invariant, defined as the absolute deviation of the eigenvalues of the distance matrix of the graph. Two graphs of the same order are said to be distance equienergetic if they have equal distance energy, while they have distinct spectra of their distance matrices. Examples of pairs of distance equienergetic graphs appear in the literature already, but most of them have diameter two only. We describe here the distance spectrum of a special composition of regular graphs, and, as an application, we show that for any ▫$n \ge 3$▫, there exists a set of ▫$n + 1$▫ distance equienergetic graphs which have order ▫$6n$▫ and diameter ▫$n - 1$▫ each.
Najdeno v: ključnih besedah
Povzetek najdenega: ...Distance energy of a graph is a recent energy-type invariant, defined as...
Ključne besede: graph theory, distance spectrum, distance energy, join, regular graphs
Objavljeno: 15.10.2013; Ogledov: 1479; Prenosov: 62
URL Polno besedilo (0,00 KB)

26.
On cubic biabelian graphs
István Kovács, 2010, objavljeni povzetek znanstvenega prispevka na konferenci

Najdeno v: ključnih besedah
Povzetek najdenega: ... graph theory, ...
Ključne besede: graph theory
Objavljeno: 15.10.2013; Ogledov: 1549; Prenosov: 11
URL Polno besedilo (0,00 KB)

27.
The strongly distance-balanced property of the generalized Petersen graphs
Klavdija Kutnar, Aleksander Malnič, Dragan Marušič, Štefko Miklavič, 2009, izvirni znanstveni članek

Opis: A graph ▫$X$▫ is said to be strongly distance-balanced whenever for any edge ▫$uv$▫ of ▫$X$▫ and any positive integer ▫$i$▫, the number of vertices at distance ▫$i$▫ from ▫$u$▫ and at distance ▫$i + 1$▫ from ▫$v$▫ is equal to the number of vertices at distance ▫$i + 1$▫ from ▫$u$▫ and at distance ▫$i$▫ from ▫$v$▫. It is proven that for any integers ▫$k \ge 2$▫ and ▫$n \ge k^2 + 4k + 1$▫, the generalized Petersen graph GP▫$(n, k)$▫ is not strongly distance-balanced.
Najdeno v: ključnih besedah
Povzetek najdenega: ...A graph ▫$X$▫ is said to be strongly distance-balanced...
Ključne besede: graph, strongy distance-balanced, generalized Petersen graph
Objavljeno: 15.10.2013; Ogledov: 1488; Prenosov: 64
URL Polno besedilo (0,00 KB)

28.
The V Latin-American Algorithms, Graphs, and Optimization Symposium
2009, zbornik recenziranih znanstvenih prispevkov na mednarodni ali tuji konferenci

Najdeno v: ključnih besedah
Povzetek najdenega: ...algorithms, graph theory, mathematical optimization, international conferences, ...
Ključne besede: algorithms, graph theory, mathematical optimization, international conferences
Objavljeno: 15.10.2013; Ogledov: 1163; Prenosov: 26
URL Polno besedilo (0,00 KB)

29.
Covering space techniques in graph theory
Aleksander Malnič, 2010, objavljeni povzetek znanstvenega prispevka na konferenci

Najdeno v: ključnih besedah
Ključne besede: graph theory, graph covers, lifting automorphisms
Objavljeno: 15.10.2013; Ogledov: 1924; Prenosov: 28
URL Polno besedilo (0,00 KB)
Gradivo ima več datotek! Več...

30.
The plane-width of graphs
Marcin Kamiński, Paul Medvedev, Martin Milanič, 2011, izvirni znanstveni članek

Najdeno v: ključnih besedah
Povzetek najdenega: ...plane-width, realization of a graph, packing non-overlapping unit disks, chromatic number, circular...
Ključne besede: plane-width, realization of a graph, packing non-overlapping unit disks, chromatic number, circular chromatic number
Objavljeno: 15.10.2013; Ogledov: 1193; Prenosov: 34
URL Polno besedilo (0,00 KB)

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