Now showing items 1-17 of 17
| Abstract: | In this paper some properties of fuzzy bridges are studied.A characterization of fuzzy trees is obtained using these concepts. |
| URI: | http://dyuthi.cusat.ac.in/purl/2860 |
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| Dyuthi-P00403.pdf | (314.0Kb) |
| Abstract: | A graphs G is clique irreducible if every clique in G of size at least two,has an edge which does not lie in any other clique of G and is clique reducible if it is not clique irreducible. A graph G is clique vertex irreducible if every clique in G has a vertex which does not lie in any other clique of G and clique vertex reducible if it is not clique vertex irreducible. The clique vertex irreducibility and clique irreducibility of graphs which are non-complete extended p-sums (NEPS) of two graphs are studied. We prove that if G(c) has at least two non-trivial components then G is clique vertex reducible and if it has at least three non-trivial components then G is clique reducible. The cographs and the distance hereditary graphs which are clique vertex irreducible and clique irreducible are also recursively characterized. |
| URI: | http://dyuthi.cusat.ac.in/purl/2859 |
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| Dyuthi-P00402.pdf | (168.7Kb) |
| Abstract: | In this paper, two notions, the clique irreducibility and clique vertex irreducibility are discussed. A graph G is clique irreducible if every clique in G of size at least two, has an edge which does not lie in any other clique of G and it is clique vertex irreducible if every clique in G has a vertex which does not lie in any other clique of G. It is proved that L(G) is clique irreducible if and only if every triangle in G has a vertex of degree two. The conditions for the iterations of line graph, the Gallai graphs, the anti-Gallai graphs and its iterations to be clique irreducible and clique vertex irreducible are also obtained. |
| URI: | http://dyuthi.cusat.ac.in/purl/615 |
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| vijaya kumar maths.pdf | (231.6Kb) |
| Abstract: | The concept of convex extendability is introduced to answer the problem of finding the smallest distance convex simple graph containing a given tree. A problem of similar type with respect to minimal path convexity is also discussed. |
| URI: | http://dyuthi.cusat.ac.in/purl/2861 |
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| Dyuthi-P00404.pdf | (88.02Kb) |
| Abstract: | Abstract. The edge C4 graph E4(G) of a graph G has all the edges of Gas its vertices, two vertices in E4(G) are adjacent if their corresponding edges in G are either incident or are opposite edges of some C4. In this paper, characterizations for E4(G) being connected, complete, bipartite, tree etc are given. We have also proved that E4(G) has no forbidden subgraph characterization. Some dynamical behaviour such as convergence, mortality and touching number are also studied |
| URI: | http://dyuthi.cusat.ac.in/purl/1534 |
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| the edge C4 graph of a graph.PDF | (2.249Mb) |
| Abstract: | The energy of a graph G is the sum of the absolute values of its eigenvalues. In this paper, we study the energies of some classes of non-regular graphs. Also the spectrum of some non-regular graphs and their complements are discussed. |
| URI: | http://dyuthi.cusat.ac.in/xmlui/purl/2038 |
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| Energies of some non regular...pdf | (143.7Kb) |
| Abstract: | Abstract. The paper deals with graph operators-the Gallai graphs and the anti-Gallai graphs. We prove the existence of a finite family of forbidden subgraphs for the Gallai graphs and the anti-Gallai graphs to be H-free for any finite graph H. The case of complement reducible graphs-cographs is discussed in detail. Some relations between the chromatic number, the radius and the diameter of a graph and its Gallai and anti-Gallai graphs are also obtained. |
| URI: | http://dyuthi.cusat.ac.in/purl/1538 |
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| Gallai and anti-gallai graphs of graph.PDF | (4.252Mb) |
| Abstract: | Eigenvalue of a graph is the eigenvalue of its adjacency matrix. The energy of a graph is the sum of the absolute values of its eigenvalues. In this note we obtain analytic expressions for the energy of two classes of regular graphs. |
| URI: | http://dyuthi.cusat.ac.in/purl/627 |
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| A_Note_on_energy_of_some_graphs.pdf | (324.8Kb) |
| Abstract: | The D-eigenvalues of a graph G are the eigenvalues of its distance matrix D, and the D-energy ED(G) is the sum of the absolute values of its D-eigenvalues. Two graphs are said to be D-equienergetic if they have the same D-energy. In this note we obtain bounds for the distance spectral radius and D-energy of graphs of diameter 2. Pairs of equiregular D-equienergetic graphs of diameter 2, on p = 3t + 1 vertices are also constructed. |
| URI: | http://dyuthi.cusat.ac.in/purl/1537 |
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| On distance energy of graphs.PDF | (2.514Mb) |
| Abstract: | this paper, the median and the antimedian of cographs are discussed. It is shown that if G, and G2 are any two cographs, then there is a cograph that is both Eulerian and Hamiltonian having Gl as its median and G2 as its antimedian. Moreover, the connected planar and outer planar cographs are characterized and the median and antimedian graphs of connected, planar cographs are listed. |
| URI: | http://dyuthi.cusat.ac.in/purl/1536 |
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| On the median and the antimedian of a cograph.PDF | (2.692Mb) |
| Abstract: | We define a new graph operator called the P3 intersection graph, P3(G)- the intersection graph of all induced 3-paths in G. A characterization of graphs G for which P-3 (G) is bipartite is given . Forbidden subgraph characterization for P3 (G) having properties of being chordal , H-free, complete are also obtained . For integers a and b with a > 1 and b > a - 1, it is shown that there exists a graph G such that X(G) = a, X(P3( G)) = b, where X is the chromatic number of G. For the domination number -y(G), we construct graphs G such that -y(G) = a and -y (P3(G)) = b for any two positive numbers a > 1 and b. Similar construction for the independence number and radius, diameter relations are also discussed. |
| URI: | http://dyuthi.cusat.ac.in/purl/1531 |
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| Utilities Mathematica.PDF | (5.904Mb) |
| Abstract: | The eigenvalue of a graph is the eigenvalue of its adjacency matrix . A graph G is integral if all of its cigenvalues are integers. In this paper some new classes of integral graphs are constructed. |
| URI: | http://dyuthi.cusat.ac.in/purl/1535 |
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| Some new integral graphs.PDF | (3.692Mb) |
| URI: | http://dyuthi.cusat.ac.in/purl/1028 |
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| Vijayakumar A 1986.pdf | (373.4Kb) |
| Abstract: | This thesis is an attempt to initiate the development of a discrete geometry of the discrete plane H = {(qmxo,qnyo); m,n e Z - the set of integers}, where q s (0,1) is fixed and (xO,yO) is a fixed point in the first quadrant of the complex plane, xo,y0 ¢ 0. The discrete plane was first considered by Harman in 1972, to evolve a discrete analytic function theory for geometric difference functions. We shall mention briefly, through various sections, the principle of discretization, an outline of discrete a alytic function theory, the concept of geometry of space and also summary of work done in this thesis |
| Description: | Department of Mathematics and Statistics,Cochin University of Science & Technology |
| URI: | http://dyuthi.cusat.ac.in/purl/3347 |
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| Dyuthi-T1328.pdf | (3.633Mb) |
| URI: | http://dyuthi.cusat.ac.in/purl/1659 |
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| Dyuthi-T0023.pdf | (3.315Mb) |
| Abstract: | In this thesis an attempt to develop the properties of basic concepts in fuzzy graphs such as fuzzy bridges, fuzzy cutnodes, fuzzy trees and blocks in fuzzy graphs have been made. The notion of complement of a fuzzy graph is modified and some of its properties are studied. Since the notion of complement has just been initiated, several properties of G and G available for crisp graphs can be studied for fuzzy graphs also. Mainly focused on fuzzy trees defined by Rosenfeld in [10] , several other types of fuzzy trees are defined depending on the acyclicity level of a fuzzy graph. It is observed that there are selfcentered fuzzy trees. Some operations on fuzzy graphs and prove that complement of the union two fuzzy graphs is the join of their complements and complement of the join of two fuzzy graphs is union of their complements. The study of fuzzy graphs made in this thesis is far from being complete. The wide ranging applications of graph theory and the interdisciplinary nature of fuzzy set theory, if properly blended together could pave a way for a substantial growth of fuzzy graph theory. |
| URI: | http://dyuthi.cusat.ac.in/purl/43 |
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| Dyuthi-T0027.pdf | (2.557Mb) |
| URI: | http://dyuthi.cusat.ac.in/purl/1698 |
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| Dyuthi-T0259.pdf | (1.520Mb) |
Now showing items 1-17 of 17
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