Dominating the Direct Product of Two Graphs through Total Roman Strategies

Given a graphGwithout isolated vertices, a total Roman dominating function forGis a function f:V(G)->{0,1,2}such that every vertexuwithf(u)=0is adjacent to a vertexvwithf(v)=2, and the set of vertices with positive labels induces a graph of minimum degree at least one. The total Roman domination number gamma tR(G)ofGis the smallest possible value of n-ary sumation v is an element of V(G)f(v)among all total Roman dominating functionsf. The total Roman domination number of the direct productGxHof the graphsGandHis studied in this work. Specifically, several relationships, in the shape of upper and lower bounds, between gamma tR(GxH)and some classical domination parameters for the factors are given. Characterizations of the direct product graphsGxHachieving small values (<= 7) for gamma tR(GxH)are presented, and exact values for gamma tR(GxH)are deduced, while considering various specific direct product classes

Vertex Sequences in Graphs

We consider a variety of types of vertex sequences, which are defined in terms of a requirement that the next vertex in the sequence must meet. For example, let S = (v1, v2, …, vk ) be a sequence of distinct vertices in a graph G such that every vertex vi in S dominates at least one vertex in V that is not dominated by any of the vertices preceding it in the sequence S. Such a sequence of maximal length is called a dominating sequence since the set {v1, v2, …, vk } must be a dominating set of G. In this paper we survey the literature on dominating and other related sequences, and propose for future study several new types of vertex sequences, which suggest the beginning of a theory of vertex sequences in graphs

On the {2}-domination number of graphs

[EN] Let G be a nontrivial graph and k ¿ 1 an integer. Given a vector of nonnegative integers w = (w0,...,wk), a function f : V(G) ¿ {0,..., k} is a w-dominating function on G if f(N(v)) ¿ wi for every v ¿ V(G) such that f(v) = i. The w-domination number of G, denoted by ¿w(G), is the minimum weight ¿(f) = ¿v¿V(G) f(v) among all w-dominating functions on G. In particular, the {2}- domination number of a graph G is defined as ¿{2} (G) = ¿(2,1,0) (G). In this paper we continue with the study of the {2}-domination number of graphs. In particular, we obtain new tight bounds on this parameter and provide closed formulas for some specific families of graphs.Cabrera-Martínez, A.; Conchado Peiró, A. (2022). On the {2}-domination number of graphs. AIMS Mathematics. 7(6):10731-10743. https://doi.org/10.3934/math.202259910731107437

On location, domination and information retrieval

The thesis is divided into two main branches: identifying and locatingdominating codes, and information retrieval. The former topics are motivated by the aim to locate objects in sensor networks (or other similar applications) and the latter one by the need to retrieve information in memories such as DNA data storage systems. Albeit the underlying applications, the study on these topics mainly belongs to discrete mathematics; more specically, to the elds of coding and graph theory. The sensor networks are usually represented by graphs where vertices represent the monitored locations and edges the connections between the locations. Moreover, the locations of the sensors are determined by a code. Furthermore, the desired properties of the sensor network are deeply linked with the properties of the underlying code. The number of errors in reading the data is abundant in the DNA data storage systems. In particular, there can occur more errors than a reasonable error-correcting code can handle. However, this problem is somewhat oset by the possibility to obtain multiple approximations of the same information from the data storage. Hence, the information retrieval process can be modelled by the Levenshtein's channel model, where a message is sent through multiple noisy channels and multiple outputs are received. In the rst two papers of the thesis, we introduce and study the new concepts of self- and solid-locating-dominating codes as a natural analogy to self-identifying codes with respect to locating-dominating codes. The rst paper introduces these new codes and considers them in some graphs such as the Hamming graphs. Then, in the second paper, we broaden our view on the topic by considering graph theoretical questions. We give optimal codes in multiple dierent graph classes and some more general results using concepts such as the Dilworth number and graph complements. The third paper focuses on the q-ary Hamming spaces. In particular, we disprove a conjecture proposed by Goddard and Wash related to identifying codes. In the fourth paper, we return to self- and solid-locating-dominating codes and give optimal codes in some graph classes and consider their densities in innite graphs. In the fth paper, we consider information retrieval in memories; in particular, the Levenshtein's channel model. In the channel model, we transmit some codeword belonging to the binary Hamming space through multiple identical channels. With the help of multiple dierent outputs, we give a list of codewords which may have been sent. In the paper, we study the number of channels required to have a rather small (constant) list size when the properties of the channels, the code and the dimension of the Hamming space are xed. In particular, we give an exact relation between the number of channels and the asymptotic value of the maximum list size.Väitöskirja käsittelee kahta aihetta: identioivia ja paikantavia peittokoodeja sekä tiedon noutamista muistista. Ensimmäisen aiheen motivaationa on objektien paikantaminen sensoriverkoista (sekä muut samankaltaiset sovellukset) ja jälkimmäisen tiedonnouto DNA-muisteista. Näiden aiheiden tutkimus kuuluu diskreettiin matematiikkaan, täsmällisemmin koodaus- ja graa-teoriaan. Sensoriverkkoja kuvataan yleensä graafeilla, joissa solmut esittävät tarkkailtuja kohteita ja viivat yhteyksiä näiden kohteiden välillä. Edelleen sensorien paikat määräytyvät annetun koodin perusteella. Tästä johtuen sensoriverkon halutut ominaisuudet pohjautuvat vahvasti alla olevaan koodiin. Luettaessa tietoa DNA-muisteista tapahtuvien virheiden määrä saattaa olla erittäin suuri; erityisesti suurempi kuin kiinnitetyn virheitä korjaavan koodin korjauskyky. Toisaalta tilanne ei ole aivan näin ongelmallinen, sillä DNA-muisteista voidaan saada useita eri arvioita muistiin tallennetusta tiedosta. Näistä syistä johtuen tietojen noutamista DNA-muisteista voidaan mallintaa käyttäen Levenshteinin kanavamallia. Kanavamallissa yksi viesti lähetetään useiden häiriöisten kanavien kautta ja näin vastaanotetaan useita viestejä (yksi jokaisesta kanavasta). Väitöskirjan kahdessa ensimmäisessä julkaisussa esitellään ja tutkitaan uusia paikantavien peittokoodien luokkia, jotka pohjautuvat aiemmin tutkittuihin itse-identioiviin koodeihin. Ensimmäisessä julkaisussa on esitelty nämä koodiluokat sekä tutkittu niitä joissain graafeissa kuten Hammingin graafeissa. Tämän jälkeen toisessa julkaisussa käsitellään yleisiä graa-teoreettisia kysymyksiä. Julkaisussa esitetään optimaaliset koodit useille graaperheille sekä joitain yleisempiä tuloksia käyttäen mm. Dilworthin lukua sekä graakomplementteja. Kolmas julkaisu keskittyy q-arisiin Hammingin avaruuksiin. Erityisesti julkaisussa todistetaan vääräksi Goddardin ja Washin aiemmin esittämä identioivia koodeja koskeva otaksuma. Neljäs artikkeli käsittelee jo kahdessa ensimmäisessä artikkelissa esiteltyjä paikantavien peittokoodien luokkia. Artikkeli esittää optimaalisia koodeja useille graaperheille sekä käsittelee äärettömiä graafeja. Viides artikkeli käsittelee tiedonnoutoa ja erityisesti Levenshteinin kanavamallia. Kanavamallissa binääriseen Hammingin avaruuteen kuuluva koodisana lähetetään useiden identtisten kanavien läpi. Näistä kanavista vastaanotetaan useita eri arvioita lähetetystä koodisanasta ja rakennetaan lista mahdollisesti lähetetyistä sanoista. Artikkelissa tutkitaan kuinka monta kanavaa tarvitaan, jotta tämän listan koko on pieni (vakio), kun kanavien ominaisuudet, koodi ja Hammingin avaruuden dimensio on kiinnitetty. Erityisesti löydetään täsmällinen suhde kanavien lukumäärän ja asymptoottisesti maksimaalisen listan koon välille

Department of Applied Mathematics Academic Program Review, Self Study / June 2010

The Department of Applied Mathematics has a multi-faceted mission to provide an exceptional mathematical education focused on the unique needs of NPS students, to conduct relevant research, and to provide service to the broader community. A strong and vibrant Department of Applied Mathematics is essential to the university's goal of becoming a premiere research university. Because research in mathematics often impacts science and engineering in surprising ways, the department encourages mathematical explorations in a broad range of areas in applied mathematics with specific thrust areas that support the mission of the school

Structural Assembly Demonstration Experiment (SADE)

The purpose of the Structural Assembly Demonstration Experiment (SADE) was to create a near-term Shuttle flight experiment focusing on the deployment and erection of structural truss elements. The activities of the MIT Space Systems Laboratory consist of three major areas: preparing and conducting neutral buoyancy simulation test series; producing a formal SADE Experiment plan; and studying the structural dynamics issues of the truss structure. Each of these areas is summarized

Industrial competitiveness of the auto parts industries in four large Asian countries : the role of government policy in a challenging international environment

Rationalization and stabilization following the Asian financial crisis of the late 1990s combined with the expansion and liberalization of regional and global trade to create significant parts industries in China, Indonesia, and the Republic of Korea. Conventional policies of stabilization and liberalization, however, cannot fully explain growth patterns. Japan and Korea grewinto major players before liberalizing trade and investment, while even after extensive liberalization Indonesia has yet to move from extensive to intensive growth. These anomalies suggest that to explain success in the auto parts industry we need to move beyond liberalization to look at policies and institutions promoting economies of scale, skill formation, quality upgrading, supplier-linkage cooperation, and innovation. In Japan, the regional and global leader, innovative assemblers led industrial development and supported key suppliers, but the government also supported diffusion of quality control techniques and new technology to small and medium enterprises, and encouraged stable employment among core employees. Korea remains weaker on both small and medium enterprise and employment fronts, but government-encouraged consolidation around a small number of business groups, an extended period of protection, and support for export promotion led to economies of scale. Liberalization of foreign investment after the financial crisis helped ameliorate the excessive statism of earlier policies and strengthened the parts industry. In China, liberalization for WTO entry, rapid expansion in demand, and strong support by local governments encouraged a wave of foreign investment in both assembly and parts. In contrast, institutional weaknesses continue to constrain development opportunities in Indonesia.Technology Industry,Economic Theory&Research,Water and Industry,Markets and Market Access,Non Bank Financial Institutions

The structure of restrictions: a "dual-domination" over the customers in the Chinese housing market

The research tries to explore the restraints imposed on customers in the contemporary Chinese housing market from the perspective of the customers. It adopts "power" as the core concept, uses the method of content analysis, and consults primarily theories of Max Weber, James Coleman, and Pierre Bourdieu. The research uses news reports as data to present the exercise of power on the customers by the Chinese state, and uses texts of housing advertisements as data to present the latent power the Chinese real-estate developers deploys to profit from trades with customers. Put together, the customers suffer from a "dual-domination" from the state and the developers in the contemporary Chinese housing market