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Shariefuddin Pirzada

Bio: Shariefuddin Pirzada is an academic researcher from University of Kashmir. The author has contributed to research in topics: Mathematics & Combinatorics. The author has an hindex of 15, co-authored 149 publications receiving 1017 citations.


Papers
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Book
01 Jan 2012

141 citations

Journal ArticleDOI
TL;DR: In this paper, it was shown that the energy of a graph G is the sum of the absolute values of the eigenvalues of G and that E(G) is not the square root of an odd integer.
Abstract: The energy E(G) of a graph G is the sum of the absolute values of the eigenvalues of G. Bapat and Pati (Bull. Kerala Math. Assoc., 1 (2004) 129-132) proved that (a) E(G) is never an odd integer. We now show that (b) E(G) is never the square root of an odd integer. Furthermore, if r and s are integers such that r ≥ 1 and 0 ≤ s ≤ r - 1 and q is an odd integer, then E(G) cannot be of the form (2s q)1/r, a result that implies both (a) and (b) as special cases.

53 citations

Journal ArticleDOI
TL;DR: In this article, a lower bound for the Laplacian energy of a simple graph with n vertices, m edges, maximum degree Δ, average degree d = 2 m n, clique number ω has been obtained.

46 citations

Journal ArticleDOI
TL;DR: The concept of energy is extended to signed digraphs and Coulson's integral formula for energy is obtained and McClelland's inequality is extended and a sharp upper bound for the energy of asigned digraph in terms of the number of arcs is obtained.

35 citations

Posted Content
TL;DR: In this article, Coulson's integral formula for energy of signed digraphs has been obtained and an infinite family of equienergetic signed directed cycles with energy equal to zero has been constructed.
Abstract: In this paper we extend the concept of energy to signed digraphs. We obtain Coulson's integral formula for energy of signed digraphs. Formulae for energies of signed directed cycles are computed and it is shown that energy of non cycle balanced signed directed cycles increases monotonically with respect to number of vertices. Characterization of signed digraphs having energy equal to zero is given. We extend the concept of non complete extended $p$ sum (or briefly, NEPS) to signed digraphs. An infinite family of equienergetic signed digraphs is constructed. Moreover, we extend McClelland's inequality to signed digraphs and also obtain sharp upper bound for energy of signed digraph in terms the number of arcs. Some open problems are also given at the end.

34 citations


Cited by
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Book ChapterDOI
01 Jan 1993
TL;DR: The theory of graphs has broad and important applications, because so many things can be modeled by graphs, and various puzzles and games are solved easily if a little graph theory is applied.
Abstract: A graph is just a bunch of points with lines between some of them, like a map of cities linked by roads. A rather simple notion. Nevertheless, the theory of graphs has broad and important applications, because so many things can be modeled by graphs. For example, planar graphs — graphs in which none of the lines cross are— important in designing computer chips and other electronic circuits. Also, various puzzles and games are solved easily if a little graph theory is applied.

541 citations

Book ChapterDOI
25 Sep 2007

425 citations

Journal ArticleDOI
TL;DR: This is a bibliography of signed graphs and related mathematics, where work on weighted graphs are regarded as outside the scope of the bibliography — except (to some extent) when the author calls the weights "signs".
Abstract: A signed graph is a graph whose edges are labeled by signs. This is a bibliography of signed graphs and related mathematics. Several kinds of labelled graph have been called "signed" yet are mathematically very different. I distinguish four types: Group-signed graphs: the edge labels are elements of a 2-element group and are multiplied around a polygon (or along any walk). Among the natural generalizations are larger groups and vertex signs. Sign-colored graphs, in which the edges are labelled from a two-element set that is acted upon by the sign group: - interchanges labels, + leaves them unchanged. This is the kind of "signed graph" found in knot theory. The natural generalization is to more colors and more general groups — or no group. Weighted graphs, in which the edge labels are the elements +1 and -1 of the integers or another additive domain. Weights behave like numbers, not signs; thus I regard work on weighted graphs as outside the scope of the bibliography — ex cept (to some extent) when the author calls the weights "signs". Labelled graphs where the labels have no structure or properties but are called "signs" for any or no reason.

258 citations

01 Jan 2009
TL;DR: The relation between the energy and the incidence energy of graphs was studied in this paper, where it was shown that the energy of a bipartite graph G is the sum of the singular values of its adjacency matrix, and that for any proper subgraph H of the graph G, IE (G) >I E(H).
Abstract: The energy of a graph E(G), is the sum of the singular values of its adjacency matrix. We define incidence energy of the graph G, denoted by IE (G), as the sum of the singular values of its incidence matrix. We are interested to find the relation between the energy and the incidence energy of graphs. For any graph G we obtain a bipartite graph 3 G such that IE (G )= E( 3 G) 2 . Moreover we find some similar upper and lower bounds of energy for incidence energy. Finally we show that for any proper subgraph H of the graph G, IE (G) >I E(H).

151 citations

Journal ArticleDOI
24 Aug 2011-PLOS ONE
TL;DR: The investigation uncovered Small-World Network features of the Hebrew lexicon, specifically a high clustering coefficient and a scale-free distribution, and provides means to examine how words group together into semantically related ‘free categories’.
Abstract: Background Semantic memory has generated much research. As such, the majority of investigations have focused on the English language, and much less on other languages, such as Hebrew. Furthermore, little research has been done on search processes within the semantic network, even though they are abundant within cognitive semantic phenomena. Methodology/Principal Findings We examine a unique dataset of free association norms to a set of target words and make use of correlation and network theory methodologies to investigate the global and local features of the Hebrew lexicon. The global features of the lexicon are investigated through the use of association correlations – correlations between target words, based on their association responses similarity; the local features of the lexicon are investigated through the use of association dependencies – the influence words have in the network on other words. Conclusions/Significance Our investigation uncovered Small-World Network features of the Hebrew lexicon, specifically a high clustering coefficient and a scale-free distribution, and provides means to examine how words group together into semantically related ‘free categories’. Our novel approach enables us to identify how words facilitate or inhibit the spread of activation within the network, and how these words influence each other. We discuss how these properties relate to classical research on spreading activation and suggest that these properties influence cognitive semantic search processes. A semantic search task, the Remote Association Test is discussed in light of our findings.

97 citations