Let G be a finite graph on the vertex set [d] = {1, . . . , d} with the edges e1, . . . , en and K[t] = K[t1, . . . , td] the polynomial ring in d variables over a field K. The edge ring of G is the semigroup ringK[G] which is generated by those monomials t = titj such that e = {i, j} is an edge of G. Let K[x] = K[x1, . . . , xn] be the polynomial ring in n variables over K and define the surje...

Topological insulators are bulk insulators that possess robust chiral conducting states along their interfaces with normal insulators. A tremendous research effort has recently been devoted to topological insulator-based heterostructures, in which conventional proximity effects give rise to a series of exotic physical phenomena. Here we establish the potential existence of topological proximity...

ABSTRACTIntroduction: Cancer is caused by genetic abnormalities, such as mutation of ontogenesis or tumor suppressor genes which alter downstream signaling pathways and protein-protein interactions. Comparison of protein interactions in cancerous and normal cells can be of help in mechanisms of disease diagnoses and treatments. Methods: We constructed protein interaction networks of cancerous a...

one of the most fundamental features of digital image and the basic steps in image processing, analysis, pattern recognition and computer vision is the edge of an image where the preciseness and reliability of its results will affect directly on the comprehension machine system made objective world. several edge detectors have been developed in the past decades, although no single edge detector...

The lower bound for the classical Ramsey number R(4, 8) is improved from 56 to 58. The author has found a new edge coloring of K57 that has no complete graphs of order 4 in the first color, and no complete graphs of order 8 in the second color. The coloring was found using a SAT solver which is based on MiniSat and customized for solving Ramsey problems. Recently Exoo improved the lower bound f...

Stripe wear occurs when the components of hip prostheses move a sufficient distance laterally to contact the edge of the acetabular cup, causing abnormally high contact stresses. In this research, edge loading contact of prosthetic hip is analyzed in the most commonly used material pairs. The contact dimensions and maximal contact pressure are investigated in mutative normal edge loading with 3...

The two operations, deletion and contraction of an edge, on multigraphs directly lead to the Tutte polynomial which satisfies a universal problem. As observed by Brylawski [8] in terms of order relations, these operations may be interpreted as a particular instance of a general theory which involves universal invariants like the Tutte polynomial, and a universal group, called the Tutte-Grothend...

In this paper, we obtain some upper and lower bounds for the general extended energy of a graph. As an application, we obtain few bounds for the (edge) Zagreb energy of a graph. Also, we deduce a relation between Zagreb energy and edge-Zagreb energy of a graph $G$ with minimum degree $delta ge2$. A lower and upper bound for the spectral radius of the edge-Zagreb matrix is obtained. Finally, we ...

A node of valence k in an edge-to-edge tiling is a point that is the common vertex of k tiles. We show that an edge-to-edge tiling of plane by pentagons each of which has m nodes of valence 3 and 5 − m nodes of valence k has properties of (m, k) = (3, 4) or (m, k) = (4, 6) if it is normal. Then we discuss tilings by congruent convex pentagons using the properties.