CHARACTERIZATION OF SOME CLASSES OF INTEGRAL HYPERGRAPHS

is a structure H(V; E), where V = fv1; v2; :::; vng is a finite set and E = fE1;E2; :::;Emg is a family of subsets of V such that Ei 6= ; 8i 2 f1; 2; : : : ;mg and [ i Ei = V: The elements v1; v2; :::; vn are called the vertices, and the sets E1;E2; :::;Em are called the hyperedges. Several...

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主要作者: ASTUTI, MULIA
格式: Dissertations
語言:Indonesia
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spelling id-itb.:696342022-11-03T09:05:51ZCHARACTERIZATION OF SOME CLASSES OF INTEGRAL HYPERGRAPHS ASTUTI, MULIA Indonesia Dissertations adjacency matrix, Cartesian product, direct product, eigenvalues, integral hypergraphs, and strong product. INSTITUT TEKNOLOGI BANDUNG https://digilib.itb.ac.id/gdl/view/69634 is a structure H(V; E), where V = fv1; v2; :::; vng is a finite set and E = fE1;E2; :::;Emg is a family of subsets of V such that Ei 6= ; 8i 2 f1; 2; : : : ;mg and [ i Ei = V: The elements v1; v2; :::; vn are called the vertices, and the sets E1;E2; :::;Em are called the hyperedges. Several results of hypergraphs theory have been studied in the literature. We can found that the results on the hypergraph theory is a generalization of the graph theory. Biggs (1993) has interpreted the relations between some coefficients of the characteristic and the Laplacian polynomial of a graph. In the first part of this dissertation, we obtained the relations for a simple and linear hypergraph. Then we will be concerned with integral hypergraphs as a generalization of integral graphs. A hypergraph is called integral if all the eigenvalues of its adjacency matrix are integers. In general, the problem of characterizing integral hypergraphs seems to be very difficult. Since there is no general characterization (besides the definition) of these hypergraphs, the problem of finding (or characterizing) integral hypergraphs has to be treated in some special interesting classes of hypergraphs. In this dissertation, we characterize six classes of hypergraphs to be integral. These classes of hypergraphs are divided into three parts. The first part, we find two classes of hypergraph that are integral, namely projective plane of order n and complete r-uniform hypergraph. In the second part, we find a sufficient and necessary condition for three classes of hypergraph that are integral. The classes of hypergraph are hyperstars, sunflower hypergraphs, and complete tripartite hypergraph. In the third part, we show a class of hypergraph which is not integral, namely hyper-regular. Hypergraph products have been a good way to construct a larger hypergraph from small ones. The most commonly studied hypergraph products are Cartesian product, direct product and strong product. In this dissertation, we characterize these hypergraph products to be integral. We prove that these three operations preserve the integrality. text
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description is a structure H(V; E), where V = fv1; v2; :::; vng is a finite set and E = fE1;E2; :::;Emg is a family of subsets of V such that Ei 6= ; 8i 2 f1; 2; : : : ;mg and [ i Ei = V: The elements v1; v2; :::; vn are called the vertices, and the sets E1;E2; :::;Em are called the hyperedges. Several results of hypergraphs theory have been studied in the literature. We can found that the results on the hypergraph theory is a generalization of the graph theory. Biggs (1993) has interpreted the relations between some coefficients of the characteristic and the Laplacian polynomial of a graph. In the first part of this dissertation, we obtained the relations for a simple and linear hypergraph. Then we will be concerned with integral hypergraphs as a generalization of integral graphs. A hypergraph is called integral if all the eigenvalues of its adjacency matrix are integers. In general, the problem of characterizing integral hypergraphs seems to be very difficult. Since there is no general characterization (besides the definition) of these hypergraphs, the problem of finding (or characterizing) integral hypergraphs has to be treated in some special interesting classes of hypergraphs. In this dissertation, we characterize six classes of hypergraphs to be integral. These classes of hypergraphs are divided into three parts. The first part, we find two classes of hypergraph that are integral, namely projective plane of order n and complete r-uniform hypergraph. In the second part, we find a sufficient and necessary condition for three classes of hypergraph that are integral. The classes of hypergraph are hyperstars, sunflower hypergraphs, and complete tripartite hypergraph. In the third part, we show a class of hypergraph which is not integral, namely hyper-regular. Hypergraph products have been a good way to construct a larger hypergraph from small ones. The most commonly studied hypergraph products are Cartesian product, direct product and strong product. In this dissertation, we characterize these hypergraph products to be integral. We prove that these three operations preserve the integrality.
format Dissertations
author ASTUTI, MULIA
spellingShingle ASTUTI, MULIA
CHARACTERIZATION OF SOME CLASSES OF INTEGRAL HYPERGRAPHS
author_facet ASTUTI, MULIA
author_sort ASTUTI, MULIA
title CHARACTERIZATION OF SOME CLASSES OF INTEGRAL HYPERGRAPHS
title_short CHARACTERIZATION OF SOME CLASSES OF INTEGRAL HYPERGRAPHS
title_full CHARACTERIZATION OF SOME CLASSES OF INTEGRAL HYPERGRAPHS
title_fullStr CHARACTERIZATION OF SOME CLASSES OF INTEGRAL HYPERGRAPHS
title_full_unstemmed CHARACTERIZATION OF SOME CLASSES OF INTEGRAL HYPERGRAPHS
title_sort characterization of some classes of integral hypergraphs
url https://digilib.itb.ac.id/gdl/view/69634
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