On Total Irregularity Strength of Double-Star and Related Graphs

AbstractLet G = (V, E) be a simple and undirected graph with a vertex set V and an edge set E. A totally irregular total k-labeling f : V ∪ E → {1, 2,. . ., k} is a labeling of vertices and edges of G in such a way that for any two different vertices x and x1, their weights and are distinct, and for any two different edges xy and x1y1 their weights f (x) + f (xy) + f (y) and f (x1) + f (x1y1) + f (y1) are also distinct. A total irregularity strength of graph G, denoted byts(G), is defined as the minimum k for which G has a totally irregular total k-labeling. In this paper, we determine the exact value of the total irregularity strength for double-star S n,m, n, m ≥ 3 and graph related to it, that is a caterpillar S n,2,n, n ≥ 3. The results are and ts(S n,2,n) = n

TOTAL EDGE AND VERTEX IRREGULAR STRENGTH OF TWITTER NETWORK

Twitter data can be converted into a graph where users can represent the vertices. Then the edges can be represented as relationships between users. This research focused on determining the total edge irregularity strength (tes) and the total vertices irregularity strength (tvs) of the Twitter network. The value could be determined by finding the greatest lower bound and the smallest upper bound. The lower bound was determined by using the properties, characteristics of the Twitter network graph along with the supporting theorems from previous studies, while the upper bound is determined through the construction of the total irregular labeling function on the Twitter network. The results in this study are the tes(TW)=18 and tvs(TW)=16

SOME CARTESIAN PRODUCTS OF A PATH AND PRISM RELATED GRAPHS THAT ARE EDGE ODD GRACEFUL

Let $G$ be a connected undirected simple graph of size $q$ and let $k$ be the maximum number of its order and its size. Let $f$ be a bijective edge labeling which codomain is the set of odd integers from 1 up to $2q-1$. Then $f$ is called an edge odd graceful on $G$ if the weights of all vertices are distinct, where the weight of a vertex $v$ is defined as the sum $mod(2k)$ of all labels of edges incident to $v$. Any graph that admits an edge odd graceful labeling is called an edge odd graceful graph. In this paper, some new graph classes that are edge odd graceful are presented, namely some cartesian products of path of length two and some circular related graphs

Characterization of Neural Activity using Complex Network Theory. Application to the Identification of the Altered Neural Substrates in Schizophrenia

La esquizofrenia es un desorden psiquiátrico caracterizado por alteraciones en el pensamiento y en la capacidad de respuesta emocional. Comprende una gran variedad de síntomas, sin embargo, no está claro que todos compartan un sustrato neurológico común. Por ello, el objetivo de esta Tesis Doctoral es desarrollar un marco de referencia desde la perspectiva de la Teoría de Redes Complejas para investigar las interacciones neurales alteradas de la esquizofrenia haciendo uso de la señal electroencefalográfica. Así, dos bases de datos independientes de registros electroencefalográficos fueron registras durante una tarea cognitiva. Nuestros hallazgos son consistentes con estudios previos al tiempo que muestran una hiperactivación del intervalo de estímulo previa a una reorganización neural disminuida durante la cognición, principalmente asociado a caminos neurales secundarios. Los hallazgos de esta Tesis ponen de manifiesto la gran heterogeneidad de la esquizofrenia, posiblemente asociada a la existencia de subgrupos dentro de la misma.Departamento de Teoría de la Señal y Comunicaciones e Ingeniería TelemáticaDoctorado en Tecnologías de la Información y las Telecomunicacione

Equivalent Frame modelling of URM buildings: numerical validation and rules

Within the context of the seismic analysis of masonry buildings, the application of verification procedures based on nonlinear analyses is now widespread and requires reliable and computationally efficient modelling strategies. Among other possible techniques, the so-called \u201cEquivalent Frame Method\u201d (EFM) is one of the most used, especially in practice engineering. This simplified approach allows to describe the global in-plane behavior of the building and is based on the assumption that the nonlinear response of each wall is concentrated in specific masonry panels which are defined a priori (piers \u2013 vertical panels and spandrels \u2013masonry beams that connect piers), while the remaining portions of the wall are usually idealized as rigid nodes. Despite of the large use of these models, there are many aspects that should be considered in order to verify their actual reliability, especially with regard to their application to existing masonry buildings. These last, indeed, are characterized by many irregularities that represent very hard-to-model features, making the application of the EFM complicated and even questionable: presence of flexible diaphragms (vaults, timber floors), different quality of the connection between the orthogonal walls, complex geometries and irregular opening patterns that are the result of several modifications during the years. All these aspects lead to several modelling uncertainties, which are not adequately addressed by the seismic codes, even if most of them explicitly suggest the use of the EFM for the seismic analysis of masonry buildings. Regarding these aspects, the collaboration to research projects developed at national scale has allowed to directly experience the not negligible consequences of the adoption of different plausible modelling choices on the outcomes of the seismic design and assessment of masonry buildings. Within this context, the objective of the present research is to provide a validation of the Equivalent Frame approach with regard to some of the critical issues related to its application. In particular, the attention is focused on the first step to deal with when applying this modelling approach, that is the a priori identification of the structural elements geometry. This last is usually related to the opening pattern of the considered wall: although it is rather straightforward in presence of regular walls with openings perfectly aligned, it may result difficult and arbitrary in presence of irregular opening patterns. The criteria proposed in the literature to this aim are mainly empirical and have never been validated in a robust way, especially with regard to their application to walls with irregular opening layouts. Furthermore, since no standardized rules are provided by the codes, professional engineers can use different criteria for the identification of piers and spandrels, thus potentially obtaining different outcomes of the seismic assessment. Hence, the research here presented firstly provides a systematic comparison between the different criteria available in the literature when applied to walls with different types of irregularity in the opening layout, aiming to explore their potentialities and their limits. To this aim, nonlinear static analyses are performed on case-studies structures represented by two-story walls, making comparisons in terms of global and local response as well as damage pattern between EF models and more accurate Finite Element models, whose results are considered as the reference solution. The obtained results are useful to provide specific indications about the rules for the EF schematization to be used (or avoided) depending on the types of irregularity characterizing the wall; moreover, some possible refinements are discussed, and specific original rules are outlined. Furthermore, since the seismic design and assessment of real buildings require to perform the analyses on 3D models, where the modelling of the connections between the orthogonal walls comes into play, the deepening of this aspect is deemed necessary in the view of a robust validation of the EF model. Indeed, as highlighted also by some preliminary analyses, the modelling of the flange effect may significantly affect, depending on the adopted assumptions, the obtained structural response. Therefore, some preliminary insights about this issue have been addressed. The obtained results, even if still at initial phase, already allow to highlight some potentialities and limits of the strategies commonly used by current EF models for the modelling of URM piers with flanges, outlining possible improvements and representing the starting point for future researches

Complex Networks and Symmetry II: Reciprocity and Evolution of World Trade

We exploit the symmetry concepts developed in the companion review of this article to introduce a stochastic version of link reversal symmetry, which leads to an improved understanding of the reciprocity of directed networks. We apply our formalism to the international trade network and show that a strong embedding in economic space determines particular symmetries of the network, while the observed evolution of reciprocity is consistent with a symmetry breaking taking place in production space. Our results show that networks can be strongly affected by symmetry-breaking phenomena occurring in embedding spaces, and that stochastic network symmetries can successfully suggest, or rule out, possible underlying mechanisms.Comment: Final accepted versio