The connective eccentricity index (CEI) of a graph $G$ is defined as $\xi^{ce}(G)=\sum_{v \in V(G)}\frac{d_G(v)}{\varepsilon_G(v)}$, where $d_G(v)$ is the degree of $v$ and $\varepsilon_G(v)$ is the eccentricity of $v$. In this paper, we characterize the unique trees with the Maximum and minimum CEI among all $n$-vertex trees and $n$-vertex conjugated trees with fixed Maximum degree, respectively.

We derive a new sharp lower bound on the k-conversion number of graphs of Maximum degree k + 1. This generalizes a result of W. Staton [Induced forests in cubic graphs, Discrete Math., 49 (1984) 175{178], which established a lower bound on the k-conversion number of (k + 1)-regular graphs.

In the extension of irregularity indices, Abdo et. al. [H. Abdo, S. Brandt, D. Dimitrov, The total irregularity of a graph, Discrete Math. Theor. Comput. Sci. 16 (2014), 201{206] de ned the total irregularity of a graph G = (V; E) as irrt(G) = P   du dv   , where du denotes the vertex degree of a vertex u 2 V (G). In 1 2 u; v2V (G) this paper, we investigate the total irregularity of trees with bounded maximal degree
and state integer linear programming problem which gives standard information about extremal trees and it also calculates the index.

Objective: Anesthetic techniques like the Akinosi technique were introduced to surmount the problems of the conventional inferior alveolar nerve block (IANB) technique. This study aimed to compare the local anesthetic efficacy of IANB via the conventional and Akinosi techniques in patients presenting to the Maxillofacial Surgery Department of School of Dentistry, Shahid Beheshti University.Methods: This clinical trial was conducted on 80 candidates for bilateral extraction of mandibular molars. For each patient, local anesthesia was induced by IANB injection, which was done by the conventional technique in one side and by the Akinosi technique in the other side of the mouth. The allocation of technique to side was randomized. Time to anesthesia for the long buccal, lingual and inferior alveolar nerves (IAN), degree of pain during injection and tooth extraction and incidence of positive aspiration in the two techniques were evaluated and analyzed using Wilcoxon Signed Rank and Chi square tests.Results: The mean time to anesthesia for the IAN was 2.82 minutes in the conventional and 3.05 minutes for the Akinosi technique. These values were 1.47 and 1.55 minutes, respectively for the lingual nerve and 1.43 and 1.56 minutes, respectively for the long buccal nerve. Four patients in the Akinosi technique and 12 patients in the conventional technique had positive aspiration. During anesthetic injection with the Akinosi technique, 72.5% were pain free, 18.8% experienced mild, 5% experienced moderate and 3.8% experienced severe pain. These values in the conventional technique were 51.3%, 27.5%, 11.3% and 10%, respectively.Conclusion: Considering the lack of a significant difference between the success rate of conventional and Akinosi IANB techniques, Akinosi technique seems to be a suitable alternative to the conventional technique since it is less painful and has lower risk of positive aspiration.

One of the ways to control the erosion in the outer bend of rivers is to use spur dikes. In recent years, the efficiency, affordability and environmental suitability of traditional spur dikes has been criticized. Therefore the importance of adopting methods which are both cost-effective and eco-friendly has been addressed. The bandal-like spur dike is a combination of a permeable and an impermeable spur dike, which is usually used in Indian Sub-Continents for riverbank protection and improvement of navigation conditions in alluvial rivers. It is made of bamboo therefore it is inexpensive and environmental friendly. In this research the effect of the permeability percentage of the bandal-like structure on the Maximum scour depth around it in a 90 degree mild bend flume and in submerged condition is investigated. Therefore a series of impermeable spur dikes (0% permeability) and bandal-like structures with (33, 50 and 64) percent permeability are placed in the flume and examined under four different Froude numbers (0. 21, 0. 23, 0. 26, 0. 29). The results showed that the Maximum scour depth around the bandal-like structure is considerably less than the Maximum scour depth around impermeable spur dikes. Also by increasing the permeability percentage of the bandal-like structures the Maximum scour depth around it decreases.

‎In this paper, we use the double counting method to find some upper bounds for the independence number of a simple graph in terms of its order, size and  Maximum degree.   Moreover,  we determine extremal graphs attaining equality in upper bounds.  In addition, some lower bounds for the energy of graphs in terms of their size and Maximum degree and the number of odd cycle, are determined.