1. On minimal forbidden subgraphs for the class of EDM-graphsGašper Jaklič, Jolanda Modic, 2015, original scientific article Abstract: 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.
Keywords: graph theory, graph, Euclidean distance matrix, distance, eigenvalue
Published in RUP: 31.12.2021; Views: 927; Downloads: 19
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2. O ekstremnih grafih z dano stopnjo in premerom/ožino : doktorska disertacijaSlobodan Filipovski, 2018, doctoral dissertation Keywords: adjacency matrix, antipodal graphs, cages, excess, defect, Ramanujan graphs, selfrepeats, degree/diameter problem, spectrum, Moore graphs, asymptotic density, distance matrices, Bermond and Bollobas problem
Published in RUP: 21.01.2019; Views: 2621; Downloads: 0 |
3. Mamart, Siwaporn: A group commutator involving the last distance matrix and dual distance matrix of a Q-polynomial distance-regular graph: the Hamming graph case. - Graphs Combin. 34 (2018), no. 4, 803--817Safet Penjić, 2018, review, book review, critique Keywords: distance-regular graph, Q-polynomial, distance matrix, dual distance matrix
Published in RUP: 21.01.2019; Views: 1511; Downloads: 15
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4. On maximal distances in a commuting graphGregor Dolinar, Bojan Kuzma, Polona Oblak, 2012, original scientific article Abstract: It is shown that matrices over algebraically closed fields that are farthest apart in the commuting graph must be non-derogatory. Rank-one matrices and diagonalizable matrices are also characterized in terms of the commuting graph.
Keywords: matematika, linearna algebra, teorija grafov, komutirajoči grafi, matrična algebra, algebraično zaprt obseg, centralizator, razdalja v grafih, mathematics, linear algebra, graph theory, commuting graph, matrix algebra, algebraically closed field, centralizer, distance in graphs
Published in RUP: 03.04.2017; Views: 2297; Downloads: 256
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5. Q-polynomial distance-regular graphs with a [sub] 1 [equal] 0 and a [sub] 2 [not equal] 0Štefko Miklavič, 2008, original scientific article Abstract: Let ▫$\Gamma$▫ denote a ▫$Q$▫-polynomial distance-regular graph with diameter ▫$D \ge 3$▫ and intersection numbers ▫$a_1=0$▫, ▫$a_2 \ne 0$▫. Let ▫$X$▫ denote the vertex set of ▫$\Gamma$▫ and let ▫$A \in {\mathrm{Mat}}_X ({\mathbb{C}})$▫ denote the adjacency matrix of ▫$\Gamma$▫. Fix ▫$x \in X$▫ and let denote $A^\ast \in {\mathrm{Mat}}_X ({\mathbb{C}})$ the corresponding dual adjacency matrix. Let ▫$T$▫ denote the subalgebra of ▫$A{\mathrm{Mat}}_X ({\mathbb{C}})$▫ generated by ▫$A$▫, ▫$A^\ast$▫. We call ▫$T$▫ the Terwilliger algebra of ▫$\Gamma$▫ with respect to ▫$x$▫. We show that up to isomorphism there exists a unique irreducible ▫$T$▫-module ▫$W$▫ with endpoint 1. We show that ▫$W$▫ has dimension ▫$2D-2$▫. We display a basis for ▫$W$▫ which consists of eigenvectors for ▫$A^\ast$▫. We display the action of ▫$A$▫ on this basis. We show that ▫$W$▫ appears in the standard module of ▫$\Gamma$▫ with multiplicity ▫$k-1$▫, where ▫$k$▫ is the valency of ▫$\Gamma$▫.
Keywords: mathematics, graph theory, adjacency matrix, distance-regular graph, Terwilliger algebra
Published in RUP: 15.10.2013; Views: 4377; Downloads: 31
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