in this paper, we first collect the earlier results about some graph operations and then wepresent applications of these results in working with chemical graphs.

In the current study, the applicability of the Annandale method was verified based on the results of silting and sediment distribution measurements carried out in eight small reservoirs, with a capacity that does not exceed 5 million m3. It was found that the application of this method is possible only in the case of small reservoirs, in which the sediment load is deposited in the near-dam zone...

In this paper, we show how formal methods of algebraic graph transformation can be made available in the technological environment of the Semantic Web. This new and promising approach allows to model and formulate transformation operations on a high level of abstraction. To demonstrate its feasibility, we develop a small book shop case study. We show how some of the necessary modification opera...

Reverse engineering (briefly RE) provides a conceptual framework for describing the process of software understanding and concept abstraction. Most RE software tools for use some form of visual representation and manipulation of the RE data. In most cases, such data consists of an attributed, multi-level, directed graph [4]. The nodes of this graph describe software artifacts at different abstr...

Temporal graphs (in which edges are active only at specified time steps) are an increasingly important and popular model for a wide variety of natural and social phenomena. We propose a new extension of classical graph modification problems into the temporal setting, and describe several variations on a modification problem in which we assign times to edges so as to maximise or minimise reachab...

Today most developers utilize source code written by other parties. Because the code is modified frequently, the developers need to grasp the impact of the modification repeatedly. A call graph and especially its special type, a call path, help the developers comprehend the modification. Source code written by other parties, however, becomes too huge to be held in memory in the form of parsed d...

The focus of this paper is two fold. Firstly, we present a logical approach to graph modification problems such as minimum node deletion, edge deletion, edge augmentation problems by expressing them as an expression in first order (FO) logic. As a consequence, it follows that these problems have constant factor polynomial-time approximation algorithms. In particular, node deletion/edge deletion...

Suppose we have a graphG in which the number of vertices distance d away from any given vertex is roughly b (in other words, our graph has a branching factor of b). An example of a graph like this is the Rubik’s cube state graph. If we have n total vertices in this graph, then we can roughly estimate the diameter of the graph to be logb n if we assume that the last layer outwards dominates the ...

Consider Bernoulli bond percolation on a locally finite, connected graph G and let pcut be the threshold corresponding to “first-moment method” lower bound. Kahn (Electron. Comm. Probab. Volume 8, 184-187. (2003)) constructed counter-example Lyons’ conjecture of pcut=pc proposed modification. Here we give positive answer Kahn’s modified question. The key observation is that in modification, new...

Abstract In recent years, Graph Neural Networks (GNNs) have achieved excellent applications in classification or prediction tasks. Recent studies demonstrated that GNNs are vulnerable to adversarial attacks. Modification Attack (GMA) and Injection (GIA) commonly attack strategies. Most graph methods based on GMA, which has a clear drawback: the attacker needs high privileges modify original gra...