Contracting edges to destroy a pattern: A complexity study

Given a graph G and an integer k, the objective of the $\Pi$-Contraction problem is to check whether there exists at most k edges in G such that contracting them in G results in a graph satisfying the property $\Pi$. We investigate the problem where $\Pi$ is `H-free' (without any induced copies of H). It is trivial that H-free Contraction is polynomial-time solvable if H is a complete graph of at most two vertices. We prove that, in all other cases, the problem is NP-complete. We then investigate the fixed-parameter tractability of these problems. We prove that whenever H is a tree, except for seven trees, H-free Contraction is W[2]-hard. This result along with the known results leaves behind three unknown cases among trees.Comment: 30 pages, 10 figures, a short version is accepted to FCT 202

Progress towards the two-thirds conjecture on locating-total dominating sets

We study upper bounds on the size of optimum locating-total dominating sets in graphs. A set $S$ of vertices of a graph $G$ is a locating-total dominating set if every vertex of $G$ has a neighbor in $S$, and if any two vertices outside $S$ have distinct neighborhoods within $S$. The smallest size of such a set is denoted by $\gamma^L_t(G)$. It has been conjectured that $\gamma^L_t(G)\leq\frac{2n}{3}$ holds for every twin-free graph $G$ of order $n$ without isolated vertices. We prove that the conjecture holds for cobipartite graphs, split graphs, block graphs, subcubic graphs and outerplanar graphs

Contracting Edges to Destroy a Pattern: A Complexity Study

Given a graph G and an integer k, the objective of the Π -Contraction problem is to check whether there exists at most k edges in G such that contracting them in G results in a graph satisfying the property Π. We investigate the problem where Π is ‘H-free’ (without any induced copies of H). It is trivial that H -free Contraction is polynomial-time solvable if H is a complete graph of at most two vertices. We prove that, in all other cases, the problem is NP-complete. We then investigate the fixed-parameter tractability of these problems. We prove that whenever H is a tree, except for seven trees, H -free Contraction is W[2]-hard. This result along with the known results leaves behind only three unknown cases among trees

Identifying codes in bipartite graphs of given maximum degree

An identifying code of a closed-twin-free graph G is a set S of vertices of G such that any two vertices in G have a distinct intersection between their closed neighborhoods and S. It was conjectured in [F. Foucaud, R. Klasing, A. Kosowski, A. Raspaud. On the size of identifying codes in triangle-free graphs. Discrete Applied Mathematics, 2012] that there exists an absolute constant c such that for every connected graph G of order n and maximum degree ∆, G admits an identifying code of size at most ∆−1 ∆ n + c. We provide significant support for this conjecture by proving it for the class of all bipartite graphs that do not contain any pairs of open-twins of degree at least 2. In particular, this class of bipartite graphs contains all trees and more generally, all bipartite graphs without 4-cycles. Moreover, our proof allows us to precisely determine the constant c for the considered class, and the list of graphs needing c > 0. For ∆ = 2 (the graph is a path or a cycle), it is long known that c = 3/2 suffices. For connected graphs in the considered graph class, for each ∆ ≥ 3, we show that c = 1/∆ ≤ 1/3 suffices and that c is required to be positive only for a finite number of trees. In particular, for ∆ = 3, there are 12 trees with diameter at most 6 with a positive constant c and, for each ∆ ≥ 4, the only tree with positive constant c is the ∆-star. Our proof is based on induction and utilizes recent results from [F. Foucaud, T. Lehtilä. Revisiting and improving upper bounds for identifying codes. SIAM Journal on Discrete Mathematics, 2022]

Low-Energy Electron Generation for Biomolecular Damage Inquiry: Instrumentation and Methods

Technological advancement has produced a variety of instruments and methods to generate electron beams that have greatly assisted in the extensive theoretical and experimental efforts devoted to investigating the effect of secondary electrons with energies approximately less than 100 eV, which are referred as low-energy electrons (LEEs). In the past two decades, LEE studies have focused on biomolecular systems, which mainly consist of DNA and proteins and their constituents as primary cellular targets of ionizing radiation. These studies have revealed that compared to other reactive species produced by high-energy radiation, LEEs have distinctive pathways and considerable efficiency in inducing lethal DNA lesions. The present work aims to briefly discuss the current state of LEE production technology and to motivate further studies and improvements of LEE generation techniques in relation to biological electron-driven processes associated with such medical applications as radiation therapy and cancer treatment

Synthesis and Characterization of Polyvinylidene-fluoride (PVDF) Nanofiber for Application as Piezoelectric Force Sensor

In the present study, PVDF nanofibers containing primarily beta-phase have been synthesized by electrospinning process. For electrospinning, a number of PVDF laden precursors were prepared varying the composition of solvents (60%-80% DMF) as well as wt% of PVDF (10wt%, 12wt%, and 15 wt% PVDF). The operating parameters for electrospinning were also varied for achieving optimal size and morphology of the PVDF nanofibers. The synthesized fibers were characterized by Fourier-transform infrared spectroscopy (FTIR), field emission scanning electron microscopy (FE-SEM), X-Ray Diffraction (XRD) and differential scanning calorimetry (DSC). PVDF with the solvent ratio of 7:3 offers beads free, thin nanofibers in comparison with other compositions. The presence of crystalline beta-phase was successfully confirmed by the XRD analysis. An exothermic peak was also observed by the DSC analysis at the temperature of 70 degrees C. PVDF nanofiber based piezoelectric force sensors were constructed and their performances were tested by applying calibrated load using a universal mechanical testing (UTM) machine and observing the resulting signal in an oscilloscope. A clear correlation was observed between the peak voltage detected by the PVDF force sensor and the applied load. The study revealed the piezoelectric property for force sensing tends to maximize (maximum current -14 mu A, initial sensitivity-160 mV/kPa) around 12 wt% of PVDF due to presence of beta-gamma phase in sample. (C) 2019 Published by Elsevier Ltd

A CFD analysis of thermal behaviour of transportation cask under fire test conditions

Thermal design of transportation cask for shipping radioactive waste needs strict compliance with the guidelines of the regulatory bodies. Lead shielding is usually provided in these casks for arresting gamma rays and reducing hazardous emissions to the environment below permissible limits. During transportation, accidental fire may break out and cause melting of lead for a prescribed duration. The present analysis reports, for the first time, a comprehensive CFD analysis of the thermal behaviour of melting of lead under high Rayleigh number convection during the fire test. The study reveals a substantial influence of natural convection on the thermal state and melting behaviour of lead which may have a great bearing on the safety and security of public during transportation of cask. (C) 2011 Elsevier B.V. All rights reserved