A note on the largest eigenvalue of non-regular graphs.
Liu, Bolian, Li, Gang (2008)
ELA. The Electronic Journal of Linear Algebra [electronic only]
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Liu, Bolian, Li, Gang (2008)
ELA. The Electronic Journal of Linear Algebra [electronic only]
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Dragoš Cvetković, Pierre Hansen, Vera Kovačević-Vujčić (2004)
The Yugoslav Journal of Operations Research
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Martín Cera, Eugenio M. Fedriani (2016)
International Journal of Applied Mathematics and Computer Science
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This paper extends to infinite graphs the most general extremal issues, which are problems of determining the maximum number of edges of a graph not containing a given subgraph. It also relates the new results with the corresponding situations for the finite case. In particular, concepts from ‘finite' graph theory, like the average degree and the extremal number, are generalized and computed for some specific cases. Finally, some applications of infinite graphs to the transportation...
Aneta Dudek, A. Paweł Wojda (2004)
Discussiones Mathematicae Graph Theory
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A graph G is said to be H-saturated if G is H-free i.e., (G has no subgraph isomorphic to H) and adding any new edge to G creates a copy of H in G. In 1986 L. Kászonyi and Zs. Tuza considered the following problem: for given m and n find the minimum size sat(n;Pₘ) of Pₘ-saturated graph of order n. They gave the number sat(n;Pₘ) for n big enough. We deal with similar problem for bipartite graphs.
Don R. Lick (1976)
Colloquium Mathematicae
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J. Nieminen (1975)
Applicationes Mathematicae
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Yuefang Sun (2017)
Discussiones Mathematicae Graph Theory
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The concept of k-connectivity κk(G), introduced by Chartrand in 1984, is a generalization of the cut-version of the classical connectivity. For an integer k ≥ 2, the k-connectivity of a connected graph G with order n ≥ k is the smallest number of vertices whose removal from G produces a graph with at least k components or a graph with fewer than k vertices. In this paper, we get a sharp upper bound for the size of G with κk(G) = t, where 1 ≤ t ≤ n − k and k ≥ 3; moreover, the unique...
Dragoš M. Cvetković, Irena Pevac (1983)
Publications de l'Institut Mathématique
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D. M. Cvetković (1975)
Matematički Vesnik
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Anton Kundrík (1990)
Mathematica Slovaca
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