New setting is introduced to study chromatic number. Neutrosophic chromatic number and chromatic number are proposed in this way, some results are obtained. Classes of neutrosophic graphs are used to obtains these numbers and the representatives of the colors. Using colors to assigns to the vertices of neutrosophic graphs is applied. Some questions and problems are posed concerning ways to do further studies on this topic. Using strong edge to define the relation amid vertices which implies having different colors amid them and as consequences, choosing one vertex as a representative of each color to use them in a set of representatives and finally, using neutrosophic cardinality of this set to compute neutrosophic chromatic number. This specific relation amid edges is necessary to compute both chromatic number concerning the number of representative in the set of representatives and neutrosophic chromatic number concerning neutrosophic cardinality of set of representatives. If two vertices have no strong edge, then they can be assigned to same color even they’ve common edge. Basic familiarities with neutrosophic graph theory and graph theory are proposed for this article.

New setting is introduced to study chromatic number. Different types of chromatic numbers and neutrosophic chromatic number are proposed in this way, some results are obtained. Classes of neutrosophic graphs are used to obtains these numbers and the representatives of the colors. Using colors to assign to the vertices of neutrosophic graphs is applied. Some questions and problems are posed concerning ways to do further studies on this topic. Using different types of edges from connectedness in same neutrosophic graphs and in modified neutrosophic graphs to define the relation amid vertices which implies having different colors amid them and as consequences, choosing one vertex as a representative of each color to use them in a set of representatives and finally, using neutrosophic cardinality of this set to compute types of chromatic numbers. This specific relation amid edges is necessary to compute both types of chromatic number concerning the number of representative in the set of representatives and types of neutrosophic chromatic number concerning neutrosophic cardinality of set of representatives. If two vertices have no intended edge, then they can be assigned to same color even they’ve common edge. Basic familiarities with neutrosophic graph theory and graph theory are proposed for this article.

New setting is introduced to study chromatic number. vital chromatic number and n-vital chromatic number are proposed in this way, some results are obtained. Classes of neutrosophic graphs are used to obtains these numbers and the representatives of the colors. Using colors to assign to the vertices of neutrosophic graphs is applied. Some questions and problems are posed concerning ways to do further studies on this topic. Using vital edge from connectedness to define the relation amid vertices which implies having different colors amid them and as consequences, choosing one vertex as a representative of each color to use them in a set of representatives and finally, using neutrosophic cardinality of this set to compute vital chromatic number. This specific relation amid edges is necessary to compute both vital chromatic number concerning the number of representative in the set of representatives and n-vital chromatic number concerning neutrosophic cardinality of set of representatives. If two vertices have no vital edge, then they can be assigned to same color even they’ve common edge. Basic familiarities with neutrosophic graph theory and graph theory are proposed for this article.

Combinatoric measures of entropy capture the complexity of a graph, but rely upon the calculation of its independent sets, or collections of non-adjacent vertices. This decomposition of the vertex set is a known NP-Complete problem and for most real world graphs is an inaccessible calculation. Recent work by Dehmer et al. and Tee et al. identified a number of alternative vertex level measures of entropy that do not suffer from this pathological computational complexity. It can be demonstrated that they are still effective at quantifying graph complexity. It is intriguing to consider whether there is a fundamental link between local and global entropy measures. In this paper, we investigate the existence of correlation between vertex level and global measures of entropy, for a narrow subset of random graphs. We use the greedy algorithm approximation for calculating the chromatic information and therefore Körner entropy. We are able to demonstrate close correlation for this subset of graphs and outline how this may arise theoretically.

For a graph G, let P(G, λ) be its chromatic polynomial. Two graphs G and H are said to be chromatically equivalent if P(G,λ) = P(H,λ). A graph is said to be chromatically unique if no other graph shares its chromatic polynomial. In this paper, chromatic polynomial of the necklace graph N_n, for n ≥ 2 has been determined. It is further shown that N₃ is chromatically unique.

The color of a thin copper oxide layer formed on a copper plate was transformed from reddish-brown into blue-purple by irradiation with 5 keV Ar+ ions to a fluence as low as 1 1015 Ar+ cm–2. In the unirradiated copper oxide layer, the copper valence state of Cu2+ as well as Cu+ and/or Cu0 was included as indicated by the presence of a shake-up satellite line in a photoemission spectrum. While for the irradiated one, the satellite line decreased in intensity, indicating that irradiation resulted in the reduction from Cu2+ to Cu+ and/or Cu0. Furthermore, nuclear reaction analysis using a 16O(d, p)17O reaction with 0.85 MeV deuterons revealed a significant loss of oxygen (51015 O atoms cm–2) in the irradiated layer. Thus, the chromatic change observed in the present work originated in the irradiation-induced reduction of a copper oxide.

The idea of strong and weak adjacencies between vertices has been generalized into fuzzy graphs and intuitionistic fuzzy graphs (IFGs) and it is an important part of making decisions. However, one or two membership degrees are not always sufficient for making decisions on real-world problems that need an answer of types “yes, neutral, and no". Consequently, in previous work, we generalized the concept into picture fuzzy graphs (PFGs) where each element in the PFG has membership, neutral, and non-membership degrees. Moreover, we constructed the notion of the coloring of PFGs based on strong and weak adjacencies between vertices. In this paper, we investigate some properties of the chromatic number of PFGs based on the concept of strong and weak adjacencies between vertices. According to the properties, we construct an algorithm to find the chromatic number of PFGs. The algorithm is usefull when we work with large PFGs. Further, we improve the method to implement the PFG’s coloring for determining traffic signal phasing at an intersection. A case study has also been done to evaluate the method.

Graph coloring is a manifestation of graph partitioning, wherein, a graph is partitioned based on the adjacency of its elements. Partitioning serves potentially as a compartmentalization for any structural problem. Vertex coloring is the heart of the problem which is to find the chromatic number of a graph. The fact that there is no general efficient solution to this problem that may work unequivocally for all graphs opens up the realistic scope for combinatorial optimization algorithms to be invoked. The algorithmic complexity of graph coloring is non-deterministic in polynomial time (NP) and hard. To the best of our knowledge, there is no algorithm as yet that procures an exact solution of the chromatic number comprehensively for any and all graphs within the polynomial (P) time domain. However, several heuristics as well as some approximation algorithms have been attempted to obtain an approximate solution for the same. Here, we present a novel heuristic, namely, the 'trailing path', which returns an approximate solution of the chromatic number within polynomial time, and, with a better accuracy than most existing algorithms. The ‘trailing path’ algorithm is effectively a subtle combination of the search patterns of two existing heuristics (DSATUR and Largest First), and, operates along a trailing path of consecutively connected nodes (and thereby effectively maps to the problem of finding spanning tree(s) of the graph) during the entire course of coloring, where essentially lies both the novelty and the apt of the current approach. The study also suggests that the judicious implementation of randomness is one of the keys towards rendering an improved accuracy in such combinatorial optimization algorithms. Apart from the algorithmic attributes, essential properties of graph partitioning in random and different structured networks have also been surveyed, followed by a comparative study. The study reveals the remarkable stability and absorptive property of chromatic number across a wide array of graphs. Finally, a case study is presented to demonstrate the potential use of graph coloring in protein design – yet another hard problem in structural and evolutionary biology.

Background/Objectives: We defined the value of a machine learning algorithm to distinguish between the EEG response to no light or any light stimulation, and between red or green light stimulation in awake volunteers with closed eyelids. This new method of EEG analysis is visionary in the understanding of visual signal processing and will facilitate anaesthetic depth research. Methods: X-gradient boosting models were used to classify the cortical response to VEP stimulation (no light vs. any light stimulation; red vs. green light stimulation). For each of the two classifications, three scenarios were tested: training and prediction in all participants (all), training and prediction in one participant (individual), training across all but one participant with prediction in the participant left out (one out). Results: Ninety-four Caucasian adults were included. The machine learning algorithm had a very high predictive value and accuracy in differentiating between no light and any light stimulation (AUCROCall: 0.96; accuracyall: 0.94; AUCROCindividual: 0.96±0.05, accuracyindividual: 0.94±0.05; AUCROConeout: 0.98±0.04; accuracyo-neout:0.96±0.04). The machine learning algorithm was highly predictive and accurate in distinguishing between green and red colour stimulation (AUCROCall: 0.97; accuracyall: 0.91; AUCROCin-dividual: 0.98±0.04, accuracyindividual: 0.96±0.04; AUCROConeout: 0.96±0.05; accuracyoneout: 0.93±0.06). The predictive value and accuracy of both classification tasks was comparable between males and females. Conclusions: Machine learning algorithms could almost continuously and reliably differentiate between the cortical EEG responses to no light or any light stimulation and between green or red colour stimulation using VEPs in awake female and male volunteers with eyes closed. Our findings may open new possibilities for using VEPs in the intraoperative setting.

A problem with synthetic aperture radar (SAR) is that, due to the poor penetrating action of electromagnetic waves inside solid bodies, the capability to observe inside distributed targets is precluded. Under these conditions, imaging action is provided only on the surface of distributed targets. The present work describes an imaging method based on the analysis of micro-movements on the Khnum-Khufu Pyramid, which are usually generated by background seismic waves. The results obtained prove to be very promising, as high-resolution full 3D tomographic imaging of the pyramid's interior and subsurface was achieved. Khnum-Khufu becomes transparent like a crystal when observed in the micro-movement domain. Based on this novelty, we have completely reconstructed internal objects, observing and measuring structures that have never been discovered before. The experimental results are estimated by processing series of SAR images from the second-generation Italian COSMO-SkyMed satellite system, demonstrating the effectiveness of the proposed method.

The adsorption of surfaces exposed to sunlight results in increased temperature that can cause physical damage and increase in energy consumption. The infrared reflective coatings that keep objects cooler have significant benefits in a wide variety of application by reflecting the infrared lights, reducing the operating costs, improving energy efficiency of buildings and vehicles (roofs, walls and windows), extend the objects’ lifespan. Our research focused on the elaboration of coatings with minimum adsorption in the infrared wavelength range. This was achieved by production of coatings that have infrared transparent and infrared reflective ability. The infrared reflection and surface warm up was investigated in the function of concentration and composition of pigments in the coatings. With investigation of different coating compositions the pigments and the binding systems were optimized. The coatings with different compositions were characterized by total solar reflection in the UV, visible and infrared wavelength range as well as by infrared reflection. Different coatings were produced in RAL7016 anthracite green color but with much better infrared reflectance, transparency as well as with heat reflectance.

The weakness of the dispersion-managed link combined with optical phase conjugation to compensate for optical signal distortion caused by chromatic dispersion and nonlinear Kerr effect of standard single mode fiber is its limited structural flexibility. We propose dispersion map that can simultaneously compensate for the distorted wavelength division multiplexed signal while increasing the configurational flexibility. Each residual dispersion per span (RDPS) in the former half of the proposed link is randomly determined, and in the latter half, the arrangement order of RDPS is the same as or inverted in the former half. We confirm that the dispersion maps in which the RDPS distribution pattern in the latter half is opposite to the arrangement order in the former half are more effective in compensation, and rather, the compensation effect is better than in the dispersion map of the conventional scheme. The notable result of this paper is that the increase of flexibility can be achieved through random arrangement of RDPS in the former half, and the compensation improvement can be achieved by through inverse arrangement in the latter half which make the distribution profile of each half link roughly symmetric with respect to the midway optical phase conjugator.