Many exact algorithms for NP-hard graph problems adopt the old Davis-Putman branch-and-reduce paradigm. The performance of these algorithms often suffers from the increasing number of graph modifications, such as deletions, that reduce the problem instance and have to be “taken back” frequently during the search process. The use of efficient data structures is necessary for fast graph modificat...

Diese Dissertation wurde selbständig, ohne unerlaubte Hilfe erarbeitet.

The computational complexity of the graph modification problems Threshold Editing and Chain has been an important open question in theory for more than 15 years. These consist adding deleting fewest possible edges to transform a into threshold or chain graph. We show that both are NP-hard, resolving conjecture by Natanzon, Shamir, Sharan from 2001. On positive side, we admit quadratic vertex ke...

Recently, knowledge graph has proved its benefits in AI applications and especially representation reasoning. Therefore, with the huge amount of published data, privacy, trust integrity take an important role to protect it from illegal access modification. In this paper, we propose PrivyKG, a new framework which uses blockchain technology along control based on preserve integrity, ensure securi...

For a graph property P, the edit distance of a graph G from P, denoted EP(G), is the minimum number of edge modifications (additions or deletions) one needs to apply to G in order to turn it into a graph satisfying P. What is the furthest graph on n vertices from P and what is the largest possible edit distance from P? Denote this maximal distance by ed(n,P). This question is motivated by algor...

An application typically has many conceptually separate pieces of behavior written over a common class graph. Each behavior makes different assumptions about the form of the class graph and the methods provided by the classes. The behaviors’ overlapping assumptions make it difficult to modify the class graph in mid-development; each modification can break assumptions that must be tracked down a...

a graph is called textit{circulant} if it is a cayley graph on a cyclic group, i.e. its adjacency matrix is circulant. let $d$ be a set of positive, proper divisors of the integer $n>1$. the integral circulant graph $icg_{n}(d)$ has the vertex set $mathbb{z}_{n}$ and the edge set e$(icg_{n}(d))= {{a,b}; gcd(a-b,n)in d }$. let $n=p_{1}p_{2}cdots p_{k}m$, where $p_{1},p_{2},cdots,p_{k}$ are disti...

0

in this paper we study the coprime graph of a group $g$. the coprime graph of a group $g$, is a graph whose vertices are elements of $g$ and two distinct vertices $x$ and $y$ are adjacent iff $(|x|,|y|)=1$. in this paper we classify all the groups which the coprime graph is a complete r-partite graph or a planar graph. also we study the automorphism group of the coprime graph.

Many real-world networks display a natural bipartite structure. It is necessary and important to study the bipartite networks by using the bipartite structure of the data. Here we propose a modification of the clustering coefficient given by the fraction of cycles with size four in bipartite networks. Then we compare the two definitions in a special graph, and the results show that the modifica...