Fixing number of co-noraml product of graphs

An automorphism of a graph $G$ is a bijective mapping from the vertex set of $G$ to itself which preserves the adjacency and the non-adjacency relations of the vertices of $G$. A fixing set $F$ of a graph $G$ is a set of those vertices of $G$ which when assigned distinct labels removes all the automorphisms of $G$, except the trivial one. The fixing number of a graph $G$, denoted by $fix(G)$, is the smallest cardinality of a fixing set of $G$. The co-normal product $G_1\ast G_2$ of two graphs $G_1$ and $G_2$, is a graph having the vertex set $V(G_1)\times V(G_2)$ and two distinct vertices $(g_1, g_2), (\acute{g_1}, \acute{g_2})$ are adjacent if $g_1$ is adjacent to $\acute{g_1}$ in $G_1$ or $g_2$ is adjacent to $\acute{g_2}$ in $G_2$. We define a general co-normal product of $k\geq 2$ graphs which is a natural generalization of the co-normal product of two graphs. In this paper, we discuss automorphisms of the co-normal product of graphs using the automorphisms of its factors and prove results on the cardinality of the automorphism group of the co-normal product of graphs. We prove that $max\{fix(G_1), fix(G_2)\}\leq fix(G_1\ast G_2)$, for any two graphs $G_1$ and $G_2$. We also compute the fixing number of the co-normal product of some families of graphs.Comment: 13 page

TSEP: Threshold-sensitive Stable Election Protocol for WSNs

Wireless Sensor Networks (WSNs) are expected to find wide applicability and increasing deployment in near future. In this paper, we propose a new protocol, Threshold Sensitive Stable Election Protocol (TSEP), which is reactive protocol using three levels of heterogeneity. Reactive networks, as opposed to proactive networks, respond immediately to changes in relevant parameters of interest. We evaluate performance of our protocol for a simple temperature sensing application and compare results of protocol with some other protocols LEACH, DEEC, SEP, ESEP and TEEN. And from simulation results it is observed that protocol outperforms concerning life time of sensing nodes used.Comment: 10th IEEE International Conference on Frontiers of Information Technology (FIT 12), 201

Simulation Analysis of Medium Access Techniques

This paper presents comparison of Access Techniques used in Medium Access Control (MAC) protocol for Wireless Body Area Networks (WBANs). Comparison is performed between Time Division Multiple Access (TDMA), Frequency Division Multiple Access (FDMA), Carrier Sense Multiple Access with Collision Avoidance (CSMA/CA), Pure ALOHA and Slotted ALOHA (S-ALOHA). Performance metrics used for comparison are throughput (T), delay (D) and offered load (G). The main goal for comparison is to show which technique gives highest Throughput and lowest Delay with increase in Load. Energy efficiency is major issue in WBAN that is why there is need to know which technique performs best for energy conservation and also gives minimum delay.Comment: NGWMN with 7th IEEE International Conference on Broadband and Wireless Computing, Com- munication and Applications (BWCCA 2012), Victoria, Canada, 201

Modeling Enhancements in DSR, FSR, OLSR under Mobility and Scalability Constraints in VANETs

Frequent topological changes due to high mobility is one of the main issues in Vehicular Ad-hoc NETworks (VANETs). In this paper, we model transmission probabilities of 802.11p for VANETs and effect of these probabilities on average transmission time. To evaluate the effect of these probabilities of VANETs in routing protocols, we select Dynamic Source Routing (DSR), Fish-eye State Routing (FSR) and Optimized Link State Routing (OLSR). Framework of these protocols with respect to their packet cost is also presented in this work. A novel contribution of this work is enhancement of chosen protocols to obtain efficient behavior. Extensive simulation work is done to prove and compare the efficiency in terms of high throughput of enhanced versions with default versions of protocols in NS-2. For this comparison, we choose three performance metrics; throughput, End-to-End Delay (E2ED) and Normalized Routing Load (NRL) in different mobilities and scalabilities. Finally, we deduce that enhanced DSR (DSR-mod) outperforms other protocols by achieving 16% more packet delivery for all scalabilities and 28% more throughput in selected mobilities than original version of DSR (DSR-orig)

Successful Surgical and Medical Management of Cesarean Scar Pregnancy in 2 Patients

Background: Cesarean scar pregnancy (CSP), once a rare entity, is on the rise due because of an increase in the cesarean section rate worldwide. Currently, there is no standard protocol available for managing CSP. To contribute to the existing literature, this article presents the current authors' experience with 2 cases of CSP that were treated successfully with two different modalities. Cases: Case 1: A 34-year-old, gravida 2, para 1, was diagnosed with a CSP on initial transvaginal ultrasound (TVUS) scan at 6 weeks of gestation. Aspiration of the gestational sac and a local injection of methotrexate was performed. After 2 weeks, the gestational sac increased in size with thinning of the CS scar (1?mm), and plateauing of the ß?human chorionic gonadotropin (ß-hCG) occurred. Laparoscopic excision of the CSP and myometrial repair resulted in resolution. Case 2: A 31-year-old, gravida 3, para 1, achieved pregnancy after a frozen?thawed embryo transfer cycle. A TVUS scan, performed at 6 weeks of gestation showed a CSP. The patient's ß-hCG level was 310 mIU/mL. Systemic methotrexate was administered intramuscularly. The patient's ß-hCG on days 4 and 7 was 260 and 252, respectively. A repeat TVUS on day 7 showed a resolving gestational sac. A second dose of methotrexate resulted in complete resolution of the CSP. Results: The treatments (aspiration, methotrexate, and laparoscopic excision for Case 1, and methotrexate for Case 2) enabled resolution of the CSPs of these 2 patients. Conclusions: Various treatment modalities have been described for managing CSP with varied levels of success. When local injection of methotrexate into the gestational sac of CSP is unsuccessful, laparoscopic removal is safe and effective. Moreover, in the presence of low levels of ?-hCG, treatment with systemic methotrexate is usually successful. (J GYNECOL SURG 30:168)Peer Reviewedhttps://deepblue.lib.umich.edu/bitstream/2027.42/140096/1/gyn.2013.0131.pd