DSpace Collection: Volume 12, Number 4 http://hdl.handle.net/10525/3857 The Collection's search engine Search the Channel search http://sci-gems.math.bas.bg/jspui/simple-search Bounds on Inverse Sum Indeg Index of Subdivision Graphs http://hdl.handle.net/10525/3862 Title: Bounds on Inverse Sum Indeg Index of Subdivision Graphs<br/><br/>Authors: Pattabiraman, Kannan<br/><br/>Abstract: The inverse sum indeg index $ISI(G)$ of a simple graph $G$ is defined as the sum of the terms $\frac{d_G(u)d_G(v)}{d_G(u)+d_G(v)}$ over all edges$uv$ of $G$, where $d_G(u)$ denotes the degree of a vertex $u$ of $G$. In this paper, we present several upper and lower bounds on the inverse sumindeg index of subdivision graphs and $t$-subdivision graphs. In addition, we obtain the upper bounds for inverse sum indeg index of$S$-sum, $S_t$-sum, $S$-product, $S_t$-product of graphs. ACM Computing Classification System (1998): G.2.2, G.2.3. A Simple Randomized 3-edge Connected Component Algorithm http://hdl.handle.net/10525/3861 Title: A Simple Randomized 3-edge Connected Component Algorithm<br/><br/>Authors: Haralampiev, Vladislav<br/><br/>Abstract: Finding the 3-edge connected components of a graph is a well-researchedproblem for which many algorithms are known. In this paper, we present a newlinear-time randomized algorithm for the problem. To the best of our knowledge,this is the first randomized algorithm for partitioning a graph into 3-edge connectedcomponents. The algorithm is a composition of simple building blocks, it is easy tounderstand and implement, and it has no corner cases. Codd’s Recommendations for Date & Time Data Types and its implementations in ISO SQL, DB2, Oracle, and Transact-SQL http://hdl.handle.net/10525/3860 Title: Codd’s Recommendations for Date & Time Data Types and its implementations in ISO SQL, DB2, Oracle, and Transact-SQL<br/><br/>Authors: Dimitrov, Vladimir<br/><br/>Abstract: Date and time data types are very important for thebusiness. From the relational model data point of view, these datatypes are simply atomic domains - their structure and operations areunimportant. After the initial introduction of the relational model ofdata and the next following implementations based on that model, Codd,in the Version 2 of relational model of data, corrected his point ofview introducing 14 recommendations about date and time data types.This paper investigate date and time data types implementations in ISOSQL, DB2, Oracle and Transact-SQL. Lagrange’s Bound on the Values of the Positive Roots of Polynomials http://hdl.handle.net/10525/3859 Title: Lagrange’s Bound on the Values of the Positive Roots of Polynomials<br/><br/>Authors: G. Akritas, Alkiviadis; W. Strzeboński, Adam; S. Vigklas, Panagiotis<br/><br/>Abstract: In this paper we present Lagrange's Joseph-Louis Lagrange,born Giuseppe Lodovico Lagrangia (25 January 1736 - 10 April 1813):Italian mathematician. theorem of 1767, for computing a bound on thevalues of the positive roots of polynomials, along with itsinteresting history and a short proof of it dating back to 1842. Sincethe bound obtained by Lagrange's theorem is of linear complexity, inthe sequel it is called ''Lagrange Linear'', or LL for short. Despite its average good performance, LL is endowed with theweaknesses inherent in all bounds with linear complexity and,therefore, the values obtained by it can be much bigger than thoseobtained by our own bound ''Local Max Quadratic'', or LMQ for short. To level the playing field, we incorporate Lagrange's theorem into ourLMQ and we present the new bound ''Lagrange Quadratic'',or LQ for short, the quadratic complexity version of LL. It turns out thatLQ is one of the most efficient bounds available since, at best, the valuesobtained by it are half of those obtained by LMQ. Empirical results indicate that when LQ replaces LMQin the Vincent-Akritas-Strzeboński Continued Fractions(VAS-CF) real root isolation method, the latter becomesmeasurably slower for some classes of polynomials. New lower bounds for the number of ACG codes over F4 http://hdl.handle.net/10525/3858 Title: New lower bounds for the number of ACG codes over F4<br/><br/>Authors: Varbanov, Zlatko; Hristova, Maya<br/><br/>Abstract: In this paper we consider additive circulant graph (ACG) codes over F4 oflength n >= 34 and we present some new results for the number of these codes.The most important result is that there exists a unique ACG code over F4 oflength 36 and minimum weight 11.