Proximity and Remoteness in Graphs: a survey

The proximity $\pi = \pi (G)$ of a connected graph $G$ is the minimum, over all vertices, of the average distance from a vertex to all others. Similarly, the maximum is called the remoteness and denoted by $\rho = \rho (G)$. The concepts of proximity and remoteness, first defined in 2006, attracted the attention of several researchers in Graph Theory. Their investigation led to a considerable number of publications. In this paper, we present a survey of the research work.Comment: arXiv admin note: substantial text overlap with arXiv:1204.1184 by other author

On the Nullity Number of Graphs

The paper discusses bounds on the nullity number of graphs. It is proved in [B. Cheng and B. Liu, On the nullity of graphs. Electron. J. Linear Algebra 16 (2007) 60--67] that $\eta \le n - D$, where $\eta$, n and D denote the nullity number, the order and the diameter of a connected graph, respectively. We first give a necessary condition on the extremal graphs corresponding to that bound, and then we strengthen the bound itself using the maximum clique number. In addition, we prove bounds on the nullity using the number of pendant neighbors in a graph. One of those bounds is an improvement of a known bound involving the domination number

The Randic index and the diameter of graphs

The {\it Randi\'c index} $R(G)$ of a graph $G$ is defined as the sum of 1/\sqrt{d_ud_v} over all edges $uv$ of $G$, where $d_u$ and $d_v$ are the degrees of vertices $u$ and $v,$ respectively. Let $D(G)$ be the diameter of $G$ when $G$ is connected. Aouchiche-Hansen-Zheng conjectured that among all connected graphs $G$ on $n$ vertices the path $P_n$ achieves the minimum values for both $R(G)/D(G)$ and $R(G)- D(G)$. We prove this conjecture completely. In fact, we prove a stronger theorem: If $G$ is a connected graph, then $R(G)-(1/2)D(G)\geq \sqrt{2}-1$, with equality if and only if $G$ is a path with at least three vertices.Comment: 17 pages, accepted by Discrete Mathematic

A Stochastic Dynamic Principle for Hybrid Systems with Execution Delay and Decision Lags

International audienceThis work presents a stochastic dynamic programming (SDP) algorithm that aims at minimizing an economic criteria based on the total energy consumption of a range extender electric vehicle (REEV). This algorithm integrates information from the REEV's navigation system in order to obtain some information about future expected vehicle speed. The model of the vehicle's energetic system, which consists of a high-voltage (HV) battery, the main energy source, and an internal combustion engine (ICE), working as an auxiliary energy source), is written as a hybrid dynamical system and the associated optimization problem in the hybrid optimal control framework. The hybrid optimal control problem includes two important physical constraints on the ICE, namely, an activation delay and a decision lag. Three methods for the inclusion of such physical constraints are studied. After introducing the SDP algorithm formulation we comment on numerical results of the stochastic algorithm and its deterministic counterpart

The relationship of selective attention and working memory with the ability to develop writing among primary school students

تهدف الدراسة الحالية إلى التعرف على علاقة الانتباه الانتقائي والذاكرة العاملة بتنمية الكتابة لدى تلاميذ المرحلة الابتدائية، حيث طبق البحث على مجموعة قوامها 10 تلاميذ، تراوحت أعمارهم ما بين 08-10 سنوات، ولتحقيق هدف الدراسة قامت الباحثتان بتطبيق رائز الانتباه "ستروب" واختبار الذاكرة العاملة، واختبار الخط. أسفرت النتائج عن وجود علاقة بين الانتباه الانتقائي والذاكرة العاملة بتنمية الكتابة لدى تلاميذ المرحلة الابتدائية.The current study aims to identify relationship of selective attention and working memory to the ability to develop writing among primary school pupils, where the research was applied to a groupe of 10 student, whose ages ranged between 08 – 12 years, and line test. The results of the study resulted in a relationship of selective attention and working memory with the ability to develop writing among primary school students

A Sharp Upper Bound on Algebraic Connectivity Using Domination Number

Abstract Let G be a connected graph of order n. The algebraic connectivity of G is the second smallest eigenvalue of the Laplacian matrix of G. A dominating set in G is a vertex subset S such that each vertex of G that is not in S is adjacent to a vertex in S. The least cardinality of a dominating set is the domination number. In this paper, we prove a sharp upper bound on the algebraic connectivity of a connected graph in terms of the domination number and characterize the associated extremal graphs. MSC: 05C35; 05C5

Cutaneous Leishmaniasis of the Lid: A Report of Nine Cases

Leishmaniasis is a parasitic disease caused by Leishmania species and is classified into three forms; cutaneous, mucocutaneous, and visceral. The eyelid is a rare site involved by leishmaniasis and only makes up 2.5% of cases with cutaneous leishmaniasis (CL). Although CL can affect both upper and lower lids on either their outer or inner aspects, the lateral canthus is most often affected. The most common aspect of lid leishmaniasis is chalazion-like lesions but ulcerous, phagedenic, cancer-like forms, and unilateral chronic granulomatous blepharitis may be observed. When the lid is involved, the disease is usually self-limiting; healing usually takes up to one year, hence early diagnosis and treatment are important. The diagnosis is based on a high index of suspicion regarding the endemicity of the disease in the region. Response to treatment in lid CL cases is quite satisfactory. In this article, we report nine cases of lid leishmaniasis with satisfactory responses to intralesional meglumine antimoniate

Chronic Exposure to Beta-Blockers Attenuates Inflammation and Mucin Content in a Murine Asthma Model

Single-dose administration of beta-adrenoceptor agonists produces bronchodilation and inhibits airway hyperresponsiveness (AHR), and is the standard treatment for the acute relief of asthma. However, chronic repetitive administration of beta-adrenoceptor agonists may increase AHR, airway inflammation, and risk of death. Based upon the paradigm shift that occurred with the use of beta-blockers in congestive heart failure, we previously determined that chronic administration of beta-blockers decreased AHR in a murine model of asthma. To elucidate the mechanisms for the beneficial effects of beta-blockers, we examined the effects of chronic administration of several beta-adrenoceptor ligands in a murine model of allergic asthma. Administration of beta-blockers resulted in a reduction in total cell counts, eosinophils, and the cytokines IL-13, IL-10, IL-5, and TGF-β1 in bronchoalveolar lavage, and attenuated epithelial mucin content and morphologic changes. The differences in mucin content also occurred if the beta-blockers were administered only during the ovalbumin challenge phase, but administration of beta-blockers for 7 days was not as effective as administration for 28 days. These results indicate that in a murine model of asthma, chronic administration of beta-blockers reduces inflammation and mucous metaplasia, cardinal features of asthma that may contribute to airflow obstruction and AHR. Similar to heart failure, our results provide a second disease model in which beta-blockers producing an acutely detrimental effect may provide a therapeutically beneficial effect with chronic administration