Displaying similar documents to “Operators approximating partial derivatives at vertices of triangulations by averaging”

Full domination in graphs

Robert C. Brigham, Gary Chartrand, Ronald D. Dutton, Ping Zhang (2001)

Discussiones Mathematicae Graph Theory

Similarity:

For each vertex v in a graph G, let there be associated a subgraph H v of G. The vertex v is said to dominate H v as well as dominate each vertex and edge of H v . A set S of vertices of G is called a full dominating set if every vertex of G is dominated by some vertex of S, as is every edge of G. The minimum cardinality of a full dominating set of G is its full domination number γ F H ( G ) . A full dominating set of G of cardinality γ F H ( G ) is called a γ F H -set of G. We study three types of full domination in...

On-line ranking number for cycles and paths

Erik Bruoth, Mirko Horňák (1999)

Discussiones Mathematicae Graph Theory

Similarity:

A k-ranking of a graph G is a colouring φ:V(G) → 1,...,k such that any path in G with endvertices x,y fulfilling φ(x) = φ(y) contains an internal vertex z with φ(z) > φ(x). On-line ranking number χ * r ( G ) of a graph G is a minimum k such that G has a k-ranking constructed step by step if vertices of G are coming and coloured one by one in an arbitrary order; when colouring a vertex, only edges between already present vertices are known. Schiermeyer, Tuza and Voigt proved that χ * r ( P ₙ ) < 3 l o g ₂ n for n ≥ 2....

On the heterochromatic number of circulant digraphs

Hortensia Galeana-Sánchez, Víctor Neumann-Lara (2004)

Discussiones Mathematicae Graph Theory

Similarity:

The heterochromatic number hc(D) of a digraph D, is the minimum integer k such that for every partition of V(D) into k classes, there is a cyclic triangle whose three vertices belong to different classes. For any two integers s and n with 1 ≤ s ≤ n, let D n , s be the oriented graph such that V ( D n , s ) is the set of integers mod 2n+1 and A ( D n , s ) = ( i , j ) : j - i ∈ 1 , 2 , . . . , n ∖ s . . In this paper we prove that h c ( D n , s ) ≤ 5 for n ≥ 7. The bound is tight since equality holds when s ∈ n,[(2n+1)/3].

On locating and differentiating-total domination in trees

Mustapha Chellali (2008)

Discussiones Mathematicae Graph Theory

Similarity:

A total dominating set of a graph G = (V,E) with no isolated vertex is a set S ⊆ V such that every vertex is adjacent to a vertex in S. A total dominating set S of a graph G is a locating-total dominating set if for every pair of distinct vertices u and v in V-S, N(u)∩S ≠ N(v)∩S, and S is a differentiating-total dominating set if for every pair of distinct vertices u and v in V, N[u]∩S ≠ N[v] ∩S. Let γ ₜ L ( G ) and γ ₜ D ( G ) be the minimum cardinality of a locating-total dominating set and a differentiating-total...

Domination Subdivision Numbers

Teresa W. Haynes, Sandra M. Hedetniemi, Stephen T. Hedetniemi, David P. Jacobs, James Knisely, Lucas C. van der Merwe (2001)

Discussiones Mathematicae Graph Theory

Similarity:

A set S of vertices of a graph G = (V,E) is a dominating set if every vertex of V-S is adjacent to some vertex in S. The domination number γ(G) is the minimum cardinality of a dominating set of G, and the domination subdivision number s d γ ( G ) is the minimum number of edges that must be subdivided (each edge in G can be subdivided at most once) in order to increase the domination number. Arumugam conjectured that 1 ≤ s d γ ( G ) ≤ 3 for any graph G. We give a counterexample to this conjecture. On the other hand,...

Superapproximation of the partial derivatives in the space of linear triangular and bilinear quadrilateral finite elements

Dalík, Josef

Similarity:

A method for the second-order approximation of the values of partial derivatives of an arbitrary smooth function u = u ( x 1 , x 2 ) in the vertices of a conformal and nonobtuse regular triangulation 𝒯 h consisting of triangles and convex quadrilaterals is described and its accuracy is illustrated numerically. The method assumes that the interpolant Π h ( u ) in the finite element space of the linear triangular and bilinear quadrilateral finite elements from 𝒯 h is known only.

Characterization of n -vertex graphs with metric dimension n - 3

Mohsen Jannesari, Behnaz Omoomi (2014)

Mathematica Bohemica

Similarity:

For an ordered set W = { w 1 , w 2 , ... , w k } of vertices and a vertex v in a connected graph G , the ordered k -vector r ( v | W ) : = ( d ( v , w 1 ) , d ( v , w 2 ) , ... , d ( v , w k ) ) is called the metric representation of v with respect to W , where d ( x , y ) is the distance between vertices x and y . A set W is called a resolving set for G if distinct vertices of G have distinct representations with respect to W . The minimum cardinality of a resolving set for G is its metric dimension. In this paper, we characterize all graphs of order n with metric dimension n - 3 .