We introduce and study a calculus for real-valued square matrices, called partial inversion, and an associated calculus for binary square matrices. The first, applied to systems of recursive linear equations, generates new sets of parameters for different types of statistical joint response models. The corresponding generating graphs are directed and acyclic. The second calculus, applied to mat...

In an investigation of percolation on isoradial graphs, we prove the criticality of canonical bond percolation on isoradial embeddings of planar graphs, thus extending celebrated earlier results for homogeneous and inhomogeneous square, triangular, and other lattices. This is achieved via the star–triangle transformation, by transporting the box-crossing property across the family of isoradial ...

In an investigation of percolation on isoradial graphs, we prove the criticality of canonical bond percolation on isoradial embeddings of planar graphs, thus extending celebrated earlier results for homogeneous and inhomogeneous square, triangular, and other lattices. This is achieved via the star–triangle transformation, by transporting the box-crossing property across the family of isoradial ...

A strong clique in a graph is intersecting all inclusion-maximal stable sets. Strong cliques play an important role the study of perfect graphs. We class diamond-free graphs, from both structural and algorithmic points view. show that following five NP -hard or co-NP problems remain when restricted to graphs: Is given strong? Does have clique? every vertex contained Given partition set into cli...

Background: Robotic needle insertion in biological tissues has been known as one the most applicable procedures in sampling, robotic injection and different medical therapies and operations.Objective: In this paper, we would like to investigate the effects of angular velocity in soft tissue insertion procedure by considering force-displacement diagram. Non-homogenous camel liver can be exploite...

In many biological systems, robustness is achieved by redundant wiring, and reflected by the presence of cycles in the graphs connecting the systems’ components. When analyzing such graphs, cyclically robust cycle bases of are of interest since they can be used to generate all cycles of a given 2-connected graph by iteratively adding basis cycles. It is known that strictly fundamental (or Kirch...

It is conjectured that connected graphs with given number of vertices and minimum spectral gap (i.e., the difference between their two largest eigenvalues) are double kite graphs. The conjecture is confirmed for connected graphs with at most 10 vertices, and, using variable neighbourhood metaheuristic, there is evidence that it is true for graphs with at most 15 vertices. Several spectral prope...

ABSTRACT Augmented marked graphs possess a special structure for modelling common resources as well as some desirable properties pertaining to liveness, boundedness, reversibility and conservativeness. This paper investigates the property-preserving composition of augmented marked graphs for the synthesis of distributed systems. It is proposed that distributed system components are specified as...

We introduce the idea of Assur graphs, a concept originally developed and exclusively employed in the literature of the kinematics community. The paper translates the terminology, questions, methods and conjectures from the kinematics terminology for one degree of freedom linkages to the terminology of Assur graphs as graphs with special properties in rigidity theory. Exploiting recent works in...

We continue the study of the following general problem on vertex colorings of graphs. Suppose that some vertices of a graph G are assigned to some colors. Can this “precoloring” be extended to a proper coloring of G with at most k colors (for some given k)? Here we investigate the complexity status of precoloring extendibility on some classes of perfect graphs, giving good characterizations (ne...