let g be a (p, q) graph. let f : v (g) → {1, 2, . . . , k} be a map. for each edge uv, assign the label gcd (f(u), f(v)). f is called k-prime cordial labeling of g if |vf (i) − vf (j)| ≤ 1, i, j ∈ {1, 2, . . . , k} and |ef (0) − ef (1)| ≤ 1 where vf (x) denotes the number of vertices labeled with x, ef (1) and ef (0) respectively denote the number of edges labeled with 1 and not labeled with 1....

The problem of finding straight-line drawings for planar graphs with small area is an important aspect in the context of drawing planar graphs and it has been extensively studied. In this thesis we will study the problem of finding planar straight-line grid drawings with minimum area. Our contributions to this problem are as follows: First, we will show, that the problem of finding minimum area...

We consider three models of sparse random graphs: undirected and directed Erdős–Rényi graphs bipartite graph with two equal parts. For such graphs, we show that if the edge connectivity probability p satisfies $$np\ge \log n+k(n)$$ $$k(n)\rightarrow \infty $$ as $$n\rightarrow , then adjacency matrix is invertible approaching one (n number vertices in former cases same for each part latter case...

In a previous work (Ozawa et al. Calc. Var. Partial Diff. Equ. 59(4), 39 2020), the authors introduced Lin-Lu-Yau type Ricci curvature for directed graphs referring to formulation of Chung Laplacian. The aim this note is provide von Renesse-Sturm characterization our lower bound via gradient estimate heat semigroup, and transportation inequality along flow. As an application, we will conclude c...

In this paper we give a method to associate a graph with an arbitrary density matrix referred to a standard orthonormal basis in the Hilbert space of a finite dimensional quantum system. We study the related issues like classification of pure and mixed states, Von-Neumann entropy, separability of multipartite quantum states and quantum operations in terms of the graphs associated with quantum s...

recently, e. m'{a}v{c}ajov'{a} and m. v{s}koviera proved that every bidirected eulerian graph which admits a nowhere zero flow, admits a nowhere zero $4$-flow. this result shows the validity of bouchet's nowhere zero conjecture for eulerian bidirected graphs. in this paper we prove the same theorem in a different terminology and with a short and simple proof. more precisely, we p...

Given noisy data, function estimation is considered when the unknown function is known a priori to consist of a small number of regions where the function is either convex or concave. When the number of regions is unknown, the model selection problem is to determine the number of convexity change points. For kernel estimates in Gaussian noise, the number of false change points is evaluated as a...

The department Image Processing at the Fraunhofer Institute for Applied Mathematics (ITWM) engages in applied research projects while also offering services to industrial customers. In order to make research results available in an industrial context quickly, a unified software framework was requested by our scientists. The presentation introduces BvLib, a software library which meets our speci...

This thesis develops new extensions to slow feature analysis (SFA) that solve supervised learning problems (e.g., classification and regression) on highdimensional data (e.g., images) in an efficient, accurate, and principled way. This type of problems has been addressed by convolutional neural networks (CNNs) in the last decade with excellent results. However, additional approaches would be va...