منابع مشابه
Character Degree Graphs That Are Complete Graphs
Let G be a finite group, and write cd(G) for the set of degrees of irreducible characters of G. We define Γ(G) to be the graph whose vertex set is cd(G) − {1}, and there is an edge between a and b if (a, b) > 1. We prove that if Γ(G) is a complete graph, then G is a solvable group.
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Graph-Partitioning problems occur in a wide range of applications. The task is to divide the vertices of a graph in equally sized parts such that as few edges as possible are crossing the boundaries. The calculation of an optimal result is NP-complete. We show a new strategy to derive upper bounds on the bisection width of graphs with regular degree. It gives optimal upper bounds for very small...
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In 1960, Dirac put forward the conjecture that r-connected 4critical graphs exist for every r ≥ 3. In 1989, Erdős conjectured that for every r ≥ 3 there exist r-regular 4-critical graphs. A method for finding r-regular 4-critical graphs and the numbers of such graphs for r ≤ 10 have been reported in [6, 7]. Results of a computer search for graphs of degree r = 12, 14, 16 are presented. All the ...
متن کاملRegular Steinhaus graphs of odd degree
A Steinhaus matrix is a binary square matrix of size n which is symmetric, with diagonal of zeros, and whose upper-triangular coefficients satisfy ai,j = ai−1,j−1+ai−1,j for all 2 6 i < j 6 n. Steinhaus matrices are determined by their first row. A Steinhaus graph is a simple graph whose adjacency matrix is a Steinhaus matrix. We give a short new proof of a theorem, due to Dymacek, which states...
متن کاملRegular Graphs of Odd Degree Are Antimagic
An antimagic labeling of a graph G with m edges is a bijection from E(G) to {1, 2, . . . ,m} such that for all vertices u and v, the sum of labels on edges incident to u differs from that for edges incident to v. Hartsfield and Ringel conjectured that every connected graph other than the single edge K2 has an antimagic labeling. We prove this conjecture for regular graphs of odd degree.
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ژورنال
عنوان ژورنال: Journal of Algebra
سال: 2014
ISSN: 0021-8693
DOI: 10.1016/j.jalgebra.2014.03.042