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1.
n-ary transit functions in graphs
Manoj Changat, Joseph Mathews, Iztok Peterin, Prasanth G. Narasimha-Shenoi, 2010, izvirni znanstveni članek

Opis: ▫$n$▫-ary transit functions are introduced as a generalization of binary (2-ary) transit functions. We show that they can be associated with convexities in natural way and discuss the Steiner convexity as a natural ▫$n$▫-ary generalization of geodesicaly convexity. Furthermore, we generalize the betweenness axioms to ▫$n$▫-ary transit functions and discuss the connectivity conditions for underlying hypergraph. Also ▫$n$▫-ary all paths transit function is considered.
Ključne besede: mathematics, graph theory, n-arity, transit function, betweenness, Steiner convexity
Objavljeno v DKUM: 31.03.2017; Ogledov: 28606; Prenosov: 327
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2.
Some Steiner concepts on lexicographic products of graphs
Bijo S. Anand, Manoj Changat, Iztok Peterin, Prasanth G. Narasimha-Shenoi, 2012, izvirni znanstveni članek

Opis: The smallest tree that contains all vertices of a subset ▫$W$▫ of ▫$V(G)$▫ is called a Steiner tree. The number of edges of such a tree is the Steiner distance of ▫$W$▫ and union of all Steiner trees of ▫$W$▫ form a Steiner interval. Both of them are described for the lexicographic product in the present work. We also give a complete answer for the following invariants with respect to the Steiner convexity: the Steiner number, the rank, the hull number, and the Carathéodory number, and a partial answer for the Radon number. At the end we locate and repair a small mistake from [J. Cáceres, C. Hernando, M. Mora, I. M. Pelayo, M. L. Puertas, On the geodetic and the hull numbers in strong product graphs, Comput. Math. Appl. 60 (2010) 3020--3031].
Ključne besede: teorija grafov, leksikografski produkt, Steinerjeva konveksnost, Steinerjeva množica, Steinerjeva razdalja, graph theory, lexicographic product, Steiner convexity, Steiner set, Steiner distance
Objavljeno v DKUM: 10.07.2015; Ogledov: 1173; Prenosov: 114
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