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The Wiener index W ( T ) is defined as the sum of distances between all pairs of vertices of the tree T . In this paper we find the variation of the Wiener index under certain tree transformations, which can be described in terms of coalescence of trees. As a consequence, conditions for...
Some recent papers for three-dimensional orthogonal graph drawing use a technique introduced by Kolmogorov and Barzdin. This technique consists of assigning x -coordinates and y -coordinates, and then computing compatible z -coordinates, which was done via vertex-colouring a conflict graph. In...
We study on-line bandwidth allocation on two parallel links. Motivated by issues of quality of service and fair resource allocation, the goal is to maximize the load of the least loaded link. We analyze several models for which we give tight bounds on the competitive ratio.
Erdős et al. (Canad. J. Math. 18 (1966) 106–112) conjecture that there exists a constant d ce such that every simple graph on n vertices can be decomposed into at most d ce n circuits and edges. We consider toroidal graphs, where the graphs can be embedded on the torus, and give a polynomial...
Let D be an acyclic digraph. The competition graph of D has the same set of vertices as D and an edge between vertices u and v if and only if there is a vertex x in D such that ( u , x ) and ( v , x ) are arcs of D . In this paper, we show that the competition graphs of doubly partial orders are...
In this paper, we show that all the coordinate functions of the advanced encryption standard (AES) round function are equivalent under an affine transformation of the input. We also show that such affine relations will always exist if the AES S-box is replaced by any bijective monomial over GF (...
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