http://dyuthi.cusat.ac.in:80/xmlui/handle/purl/478 2013-05-25T07:46:27Z http://dyuthi.cusat.ac.in:80/xmlui/handle/purl/2861 Convex extendable trees Parvathy, K S; Vijayakumar, A 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. 1999-01-01T00:00:00Z http://dyuthi.cusat.ac.in:80/xmlui/handle/purl/2860 A characterization of fuzzy trees Sunitha, M S; Vijayakumar, A In this paper some properties of fuzzy bridges are studied.A characterization of fuzzy trees is obtained using these concepts. 1999-01-01T00:00:00Z http://dyuthi.cusat.ac.in:80/xmlui/handle/purl/2859 Clique Irreducibility and Clique Vertex Irreducibility of Graphs Aparna, Lakshmanan S; Vijayakumar, A. 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. 2009-01-01T00:00:00Z http://dyuthi.cusat.ac.in:80/xmlui/handle/purl/2040 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 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. 2007-01-01T00:00:00Z