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Dr. A Krishnamoorthy [1]
Prof.(Dr) A Vijaya Kumar [17]

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Convex extendable trees

Parvathy, K S; Vijayakumar, A (Elsevier, 1999)

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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)

A characterization of fuzzy trees

Sunitha, M S; Vijayakumar, A (Elsevier, 1999)

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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)

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Dyuthi-P00403.pdf	(314.0Kb)

Clique Irreducibility and Clique Vertex Irreducibility of Graphs

Aparna, Lakshmanan S; Vijayakumar, A. (2009)

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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)

OPTIMAL UTILIZATION OF SERVICE FACILITY FOR A k-OUT-OF-n SYSTEM WITH REPAIR BY EXTENDING SERVICE TO EXTERNAL CUSTOMERS IN A RETRIAL QUEUE

Krishnamoorthy, A; Vishwanath C, Narayanan; Deepak, T G (Korean Society for Computational & Applied mathematics, 2007)

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Abstract:

In this paper, we study a k-out-of-n system with single server who provides service to external customers also. The system consists of two parts:(i) a main queue consisting of customers (failed components of the k-out-of-n system) and (ii) a pool (of finite capacity M) of external customers together with an orbit for external customers who find the pool full. An external customer who finds the pool full on arrival, joins the orbit with probability and with probability 1− leaves the system forever. An orbital customer, who finds the pool full, at an epoch of repeated attempt, returns to orbit with probability (< 1) and with probability 1 − leaves the system forever. We compute the steady state system size probability. Several performance measures are computed, numerical illustrations are provided.

URI:

http://dyuthi.cusat.ac.in/xmlui/purl/2040

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Energies of some non-regular graphs

Indulal, G; Vijayakumar, A (Springer, October , 2007)

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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)

OPTIMAL UTILIZATION OF SERVICE FACILITY FOR A k-OUT-OF-n SYSTEM WITH REPAIR BY EXTENDING SERVICE TO EXTERNAL CUSTOMERS IN A RETRIAL QUEUE

Krishnamoorthy, A; Vishwanath C, Narayanan; Deepak, T G (Korean Society for Computational & Applied mathematics, 2007)

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Abstract:

URI:

http://dyuthi.cusat.ac.in/xmlui/purl/2040

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Optimal utilization of service facility...pdf	(240.7Kb)

Energies of some non-regular graphs

Indulal, G; Vijayakumar, A (Springer, October , 2007)

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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)

GALLAI AND ANTI-GALLAI GRAPHS OF A GRAPH

LAKSHMANAN, APARNA; . RAO, S. B; Vijayakumar, A (February 4, 2010)

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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)

ON DISTANCE ENERGY OF GRAPHS

Indulal,G; Gutmanb,Ivan; Vijayakumar,A (February 4, 2010)

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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 THE MEDIAN AND THE ANTIMEDIAN OF A COGRAPH

Rao', S.B.; vijayakumar, A (February 4, 2010)

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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)

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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