Index of imprimitivity of the non-complete extended -sum of digraphs.
Petrić, M.V. (1995)
Matematichki Vesnik
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Petrić, M.V. (1995)
Matematichki Vesnik
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Weige Xi, Ligong Wang (2016)
Discussiones Mathematicae Graph Theory
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Let G = (V (G),E(G)) be a simple strongly connected digraph and q(G) be the signless Laplacian spectral radius of G. For any vertex vi ∈ V (G), let d+i denote the outdegree of vi, m+i denote the average 2-outdegree of vi, and N+i denote the set of out-neighbors of vi. In this paper, we prove that: (1) (1) q(G) = d+1 +d+2 , (d+1 ≠ d+2) if and only if G is a star digraph [...] ,where d+1, d+2 are the maximum and the second maximum outdegree, respectively [...] is the digraph on n vertices...
Adiga, C., Khoshbakht, Z. (2009)
JIPAM. Journal of Inequalities in Pure & Applied Mathematics [electronic only]
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Mieczysław Borowiecki, Danuta Michalak (1989)
Banach Center Publications
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Petrić, Milenko (1996)
Publications de l'Institut Mathématique. Nouvelle Série
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Mehdi Behzad, Frank Harary (1977)
Mathematica Slovaca
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Zdzisław Skupień (1999)
Discussiones Mathematicae Graph Theory
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Abas, M. (2000)
Acta Mathematica Universitatis Comenianae. New Series
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Peter Horák (1983)
Mathematica Slovaca
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Fu Ji Zhang, Zhibo Chen (2006)
Czechoslovak Mathematical Journal
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The study on limit points of eigenvalues of undirected graphs was initiated by A. J. Hoffman in 1972. Now we extend the study to digraphs. We prove: 1. Every real number is a limit point of eigenvalues of graphs. Every complex number is a limit point of eigenvalues of digraphs. 2. For a digraph , the set of limit points of eigenvalues of iterated subdivision digraphs of is the unit circle in the complex plane if and only if has a directed cycle. 3. Every limit point of eigenvalues...
Richard H. Hammack, Katherine E. Toman (2010)
Discussiones Mathematicae Graph Theory
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We investigate expressions of form A×C ≅ B×C involving direct products of digraphs. Lovász gave exact conditions on C for which it necessarily follows that A ≅ B. We are here concerned with a different aspect of cancellation. We describe exact conditions on A for which it necessarily follows that A ≅ B. In the process, we do the following: Given an arbitrary digraph A and a digraph C that admits a homomorphism onto an arc, we classify all digraphs B for which A×C ≅ B×C.
Hortensia Galeana-Sánchez, José de Jesús García-Ruvalcaba (2001)
Discussiones Mathematicae Graph Theory
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A digraph D is called a kernel-perfect digraph or KP-digraph when every induced subdigraph of D has a kernel. We call the digraph D an m-coloured digraph if the arcs of D are coloured with m distinct colours. A path P is monochromatic in D if all of its arcs are coloured alike in D. The closure of D, denoted by ζ(D), is the m-coloured digraph defined as follows: V( ζ(D)) = V(D), and A( ζ(D)) = ∪_{i} {(u,v) with colour i: there exists a monochromatic...