Let $G$ be a bipartite graph. In this paper we consider the two kind of location problems namely $p$-center and $p$-median problems on bipartite graphs. The $p$-center and $p$-median problems asks to find a subset of vertices of cardinality $p$, so that respectively the maximum and sum of the distances from this set to all other vertices in $G$ is minimized. For each case we present some proper...

In this paper we propose the application of the generalized median graph in a graph-based k -means clustering algorithm. In the graph-based k -means algorithm, the centers of the clusters have been traditionally represented using the set median graph. We propose an approximate method for the generalized median graph computation that allows to use it to represent the centers of the clusters. Exp...

This paper presents a new approach for region-based video mosaicing, treating moving objects separately from the background, and with improved ghost-like noise elimination. The mosaic images show the moving objects superimposed over a stationary background. Conventional technologies can reduce the ghost-like noise that occurs from moving objects by using temporal median filtering, but its effic...

Median graphs have many interesting properties. One of them is— in connection with triangle free graphs—the recognition complexity. In general the complexity is not very fast, but if we restrict to the planar case the recognition complexity becomes linear. Despite this fact, there is no characterization of planar median graphs in the literature. Here an additional condition is introduced for th...

Let G be a Q4-free median graph on n vertices and m edges. Let k be the number of equivalence classes of Djoković-Winkler’s relation Θ and let h be the number of Q3’s in G. Then we prove that 2n −m − k + h = 2. We also characterize median grid graphs in several different ways, for instance, they are the grid graphs with m− n + 1 squares. To obtain these results we introduce the notion of square...

We compare play in private and public committees when insiders care both about how well the committee decision serves organizational goals, and about the rewards which outsiders give for representing their interests. We show that a private committee reaches decisions which better serve organizational goals than either a public committee or the median insider choosing alone; and that a committee...

and was printed with financial support of the Deutsche Forschungsgemeinschaft.

The median stabilization degree (msd, for short) of a median algebra measures the largest possible number of steps needed to generate a subalgebra with an arbitrary set of generators. With computer assistance, we found that msd of the lattice {−1, 0, 1}4 equals 2. This value is of critical importance to determine msd of {−1, 0, 1}n for all n ≥ 5 and to determine msd of the free median algebra λ...

Median graphs have many interesting properties. One of them is—in connection with triangle free graphs—the recognition complexity. In general the complexity is not very fast, but if we restrict to the planar case the recognition complexity becomes linear. Despite this fact, there is no characterization of planar median graphs in the literature. Here an additional condition is introduced for the...

The corona product G ◦ H of two graphs G and H is obtained by taking one copy of G and |V (G)| copies of H; and by joining each vertex of the i-th copy of H to the i-th vertex of G, where 1 ≤ i ≤ |V (G)|. In this paper, exact formulas for the eccentric distance sum and the edge revised Szeged indices of the corona product of graphs are presented. We also study the conditions under which the cor...