Dominating functions of graphs with two values

Bohdan Zelinka

Displaying similar documents to “Dominating functions of graphs with two values”

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.

Point-set domatic numbers of graphs

Bohdan Zelinka (1999)

Mathematica Bohemica

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A subset $D$ of the vertex set $V (G)$ of a graph $G$ is called point-set dominating, if for each subset $S \subseteq V (G) - D$ there exists a vertex $v \in D$ such that the subgraph of $G$ induced by $S \cup {v}$ is connected. The maximum number of classes of a partition of $V (G)$ , all of whose classes are point-set dominating sets, is the point-set domatic number $d_{p} (G)$ of $G$ . Its basic properties are studied in the paper.

Linear integral equations in the space of regulated functions

Milan Tvrdý (1998)

Mathematica Bohemica

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n this paper we investigate systems of linear integral equations in the space $𝔾_{L}^{n}$ of $n$ -vector valued functions which are regulated on the closed interval $[0, 1]$ (i.e. such that can have only discontinuities of the first kind in $[0, 1]$ ) and left-continuous in the corresponding open interval $(0, 1) .$ In particular, we are interested in systems of the form x(t) - A(t)x(0) - 01B(t,s)[d x(s)] = f(t), where $f \in 𝔾_{L}^{n}$ , the columns of the $n \times n$ -matrix valued function $A$ belong to $𝔾_{L}^{n}$ , the entries of $B (t, .)$ have a bounded variation...

Magic powers of graphs

Marián Trenkler, Vladimír Vetchý (1997)

Mathematica Bohemica

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Necessary and sufficient conditions for a graph $G$ that its power $G^{i}$ , $i \geq 2$ , is a magic graph and one consequence are given.

On the set of solutions of the system $x_{1} + x_{2} + x_{3} = 1, x_{1} x_{2} x_{3} = 1$

Miloslav Hlaváček (1998)

Mathematica Bohemica

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A proof is given that the system in the title has infinitely many solutions of the form $a_{1} + a_{2}$ , where $a_{1}$ and $a_{2}$ are rational numbers.

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.

Displaying similar documents to “Dominating functions of graphs with two values”

Circular distance in directed graphs

Point-set domatic numbers of graphs

Linear integral equations in the space of regulated functions

Magic powers of graphs

On the set of solutions of the system x 1 + x 2 + x 3 = 1 , x 1 x 2 x 3 = 1

Spectral properties of fourth order differential operators

On the set of solutions of the system $x_{1} + x_{2} + x_{3} = 1, x_{1} x_{2} x_{3} = 1$