Abstract In this paper we study two operations of merging components in a chain graph, which appear to be elementary operations yielding an equivalent graph in the respective sense. At first, we recall basic results on the operation of feasible merging components, which is related to classic LWF Markov equivalence of chain graphs. These results are used to get a graphical characterisation of fa...

We investigate a new type of graph inequality (in the tradition of Cvetković, Simić, and Capobianco) which is based on the subgraph relation and which allows as terms fixed graphs, graph variables with specified vertices, and the operation of identifying vertices. We present a simple graph inequality which does not have a solution, and show that the solvability of inequalities with only one gra...

The paper is about the edge covers of the graph. The change in the edge covering number of the graph is observed under the operations vertex removal, edge removal and edge addition. The necessary and sufficient condition is proved under which the edge covering number decreases when a vertex is removed from the graph also when an edge is added to the graph. The necessary and sufficient condition...

An operation of concatenation is introduced for graphs. Then strings are viewed as expressions denoting graphs, and string languages are interpreted as graph languages. For a class K of string languages, Int(K) is the class of all graph languages that are interpretations of languages from K. For the class REG of regular languages, Int(REG) might be called the class of regular graph languages; i...

Reliable and accurate ultra-short-term prediction of wind power is vital for the operation optimization systems. However, volatility intermittence pose uncertainties to traditional point prediction, resulting in an increased risk system operation. To represent uncertainty power, this paper proposes a new method interval based on graph neural network (GNN) improved bootstrap technique. Specifica...

Internally, many source code analysis tools make use of graphs. For example, one of the oldest and most widely used internal graphs is the control-flow graph developed for use within a compiler. Work on compilation has also led to the development of the call graph, the procedure dependence graph (PDG), and the static-single assignment (SSA) graph. Compilers are not the only source-code analysis...

There exist two conjectures for constraint satisfaction problems (CSPs) of reducts of finitely bounded homogeneous structures: the first one states that tractability of the CSP of such a structure is, when the structure is a model-complete core, equivalent to its polymorphism clone satisfying a certain non-trivial linear identity modulo outer embeddings. The second conjecture, challenging the a...

We show that a 6-regular graph of diameter d embedded on the torus can have at most 3d + 3d+ 1 vertices having exhibited a graph of this order for each d ≥ 1. 1 6-regular Toroidal Graphs In [1] it is proven that all 6-regular toroidal graphs can have their vertices arranged in a rectangular based grid structure with parallel diagonals across every sub-rectangle in the grid. A special case of th...

This paper first considers several types of additive bases. A typical problem is to find nv(k), the largest n for which there exists a set {0 al < a2 <" < ak} Of distinct integers modulo n such that each in the range 0 =<-< n can be written at least once as mai + aj (modulo n) with </'. For example, nv(8) 24, The other problems arise if at least is changed to at most, or </' to-</', or if the w...