The diameter of an orientation of a complete multipartite graph

The diameter of an orientation of a complete multipartite graph

Optimal orientation of the tensor product of a small diameter graph and a complete graph

For a graph G, let D(G) be the set of all strong orientations of G. The orientation number of G, denoted by d(G), is defined as min{d(D) | D ∈ D(G)}, where d(D) denotes the diameter of the digraph D. In this paper, a sufficient condition is given for d(G×Kn) = d(G×Kn), where G is a graph with d(G) two or three and × is the tensor product of graphs.

The Steiner diameter of a graph

‎The Steiner distance of a graph‎, ‎introduced by Chartrand‎, ‎Oellermann‎, ‎Tian and Zou in 1989‎, ‎is a natural generalization of the‎ ‎concept of classical graph distance‎. ‎For a connected graph $G$ of‎ ‎order at least $2$ and $Ssubseteq V(G)$‎, ‎the Steiner‎ ‎distance $d(S)$ among the vertices of $S$ is the minimum size among‎ ‎all connected subgraphs whose vertex sets contain $S$‎. ‎Let $...

an investigation of the types of text reduction in subtitling: a case study of the persian film gilaneh with english subtitles

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The interval number of a complete multipartite graph

The interval number of a graph G, denoted i(G), is the least positive integer t for which G is the intersection graph of a family of sets each of which is the union of at most t cIosed intervals of the real line IR. Trotter and Harary showed that the interval number of the complete bipartite graph K(m, n) is [(mn + I)/(m + n)]. Matthews showed that the interval number of the complete multiparti...