Magic powers of graphs

Marián Trenkler; Vladimír Vetchý

Displaying similar documents to “Magic powers of graphs”

Comparison theorems for differential equations of neutral type

Miroslava Růžičková (1997)

Mathematica Bohemica

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We are interested in comparing the oscillatory and asymptotic properties of the equations $L_{n} [x (t) - P (t) x (g (t))] + δ f (t, x (h (t))) = 0$ with those of the equations $M_{n} [x (t) - P (t) x (g (t))] + δ Q (t) q (x (r (t))) = 0 .$

Circular distance in directed graphs

Bohdan Zelinka (1997)

Mathematica Bohemica

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Circular distance $d^{\circ} (x, y)$ between two vertices $x$ , $y$ of a strongly connected directed graph $G$ is the sum $d (x, y) + d (y, x)$ , where $d$ is the usual distance in digraphs. Its basic properties are studied.

Dominating functions of graphs with two values

Bohdan Zelinka (1998)

Mathematica Bohemica

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The $Y$ -domination number of a graph for a given number set $Y$ was introduced by D. W. Bange, A. E. Barkauskas, L. H. Host and P. J. Slater as a generalization of the domination number of a graph. It is defined using the concept of a $Y$ -dominating function. In this paper the particular case where $Y = {0, 1 / k}$ for a positive integer $k$ is studied.

Spectral properties of fourth order differential operators

Ondřej Došlý, Roman Hilscher (1997)

Mathematica Bohemica

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Necessary and sufficient conditions for discreteness and boundedness below of the spectrum of the singular differential operator $ℓ (y) \equiv \frac{1}{w (t)} (r (t) y)$ , $t \in [a, \infty)$ are established. These conditions are based on a recently proved relationship between spectral properties of $ℓ$ and oscillation of a certain associated second order differential equation.