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Title: Energy of Graphs and Digraphs
Researcher: Bhat, Mushtaq Ahmad
Guide(s): Pirzada, S.
Keywords: Graphs, Digraphs, Energy
Unicyclic signed graphs, Equienergetic signed graphs
University: University of Kashmir
Completed Date: NA
Abstract: In Chapter 1, we present a brief introduction of spectra of graphs and some newlinedefinitions. Chapter 2 is a brief review of energy of graphs and digraphs. We newlinestudy the problem of real numbers which cannot be the energy of a digraph. In newlineChapter 3, we study the problem of minimal energy in unicyclic signed graphs. newlineWe also construct pairs of equienergetic signed graphs. In Chapter 4, we have newlineintroduced the concept of energy in signed digraphs. We characterize unicyclic newlinesigned digraphs with minimal and maximal energy. We extend the concept of newlinenon extended p-sum (NEPS) to signed digraphs and study its spectra. We obtain newlineupper bounds for the energy of signed digraphs. We also construct pairs of non newlinecospectral equienergetic signed digraphs. In Chapter 5, we obtain a sufficient newlinecondition for the even coefficients of the characteristic polynomial of a bipartite newlinesigned digraph to alternate in sign and in this case we show it is possible to compare newlinethe energy of bipartite signed digraphs by means of a quasi-order relation defined newlineon coefficients. We also obtain a sufficient condition for all the even coe_cients newlineof a bipartite signed digraph to be nonnegative. We construct integral, real and newlineGaussian signed digraphs and qausi-cospectral digraphs. newline
Appears in Departments:Department of Mathematics

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02_certificate.pdf43.6 kBAdobe PDFView/Open
03_abstract.pdf67.18 kBAdobe PDFView/Open
04_declaration.pdf91.25 kBAdobe PDFView/Open
05_acknowledgements.pdf194.07 kBAdobe PDFView/Open
06_contents.pdf50.71 kBAdobe PDFView/Open
07_chapter1.pdf186.53 kBAdobe PDFView/Open
08_chapter2.pdf266.9 kBAdobe PDFView/Open
09_chapter3.pdf324.64 kBAdobe PDFView/Open
10_chapter4.pdf294.3 kBAdobe PDFView/Open
11_chapter5.pdf407.09 kBAdobe PDFView/Open
12_references.pdf91.61 kBAdobe PDFView/Open

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