Displaying similar documents to “On the four vertex theorem in planes with radial density e φ ( r ) ”

Mean value densities for temperatures

N. Suzuki, N. A. Watson (2003)

Colloquium Mathematicae

Similarity:

A positive measurable function K on a domain D in ℝ n + 1 is called a mean value density for temperatures if u ( 0 , 0 ) = ∫ ∫ D K ( x , t ) u ( x , t ) d x d t for all temperatures u on D̅. We construct such a density for some domains. The existence of a bounded density and a density which is bounded away from zero on D is also discussed.

On the structural result on normal plane maps

Tomás Madaras, Andrea Marcinová (2002)

Discussiones Mathematicae Graph Theory

Similarity:

We prove the structural result on normal plane maps, which applies to the vertex distance colouring of plane maps. The vertex distance-t chromatic number of a plane graph G with maximum degree Δ(G) ≤ D, D ≥ 12 is proved to be upper bounded by 6 + [ ( 2 D + 12 ) / ( D - 2 ) ] ( ( D - 1 ) ( t - 1 ) - 1 ) . This improves a recent bound 6 + [ ( 3 D + 3 ) / ( D - 2 ) ] ( ( D - 1 ) t - 1 - 1 ) , D ≥ 8 by Jendrol’ and Skupień, and the upper bound for distance-2 chromatic number.

Construction of an Uncountable Difference between Φ(B) and Φ f ( B )

Josh Campbell, David Swanson (2008)

Bulletin of the Polish Academy of Sciences. Mathematics

Similarity:

We construct a set B and homeomorphism f where f and f - 1 have property N such that the symmetric difference between the sets of density points and of f-density points of B is uncountable.

Analytic functions are ℐ -density continuous

Krzysztof Ciesielski, Lee Larson (1994)

Commentationes Mathematicae Universitatis Carolinae

Similarity:

A real function is ℐ -density continuous if it is continuous with the ℐ -density topology on both the domain and the range. If f is analytic, then f is ℐ -density continuous. There exists a function which is both C ∞ and convex which is not ℐ -density continuous.

Bounds On The Disjunctive Total Domination Number Of A Tree

Michael A. Henning, Viroshan Naicker (2016)

Discussiones Mathematicae Graph Theory

Similarity:

Let G be a graph with no isolated vertex. In this paper, we study a parameter that is a relaxation of arguably the most important domination parameter, namely the total domination number, γt(G). A set S of vertices in G is a disjunctive total dominating set of G if every vertex is adjacent to a vertex of S or has at least two vertices in S at distance 2 from it. The disjunctive total domination number, [...] γtd(G) γ t d ( G ) , is the minimum cardinality of such a set. We observe that [...] γtd(G)≤γt(G)...

Coalescing Fiedler and core vertices

Didar A. Ali, John Baptist Gauci, Irene Sciriha, Khidir R. Sharaf (2016)

Czechoslovak Mathematical Journal

Similarity:

The nullity of a graph G is the multiplicity of zero as an eigenvalue in the spectrum of its adjacency matrix. From the interlacing theorem, derived from Cauchy’s inequalities for matrices, a vertex of a graph can be a core vertex if, on deleting the vertex, the nullity decreases, or a Fiedler vertex, otherwise. We adopt a graph theoretical approach to determine conditions required for the identification of a pair of prescribed types of root vertices of two graphs to form a cut-vertex...