On the remoteness function in median graphs
نویسندگان
چکیده
منابع مشابه
On the remoteness function in median graphs
A profile on a graph G is any nonempty multiset whose elements are vertices from G. The corresponding remoteness function associates to each vertex x ∈ V (G) the sum of distances from x to the vertices in the profile. Starting from some nice and useful properties of the remoteness function in hypercubes, the remoteness function is studied in arbitrary median graphs with respect to their isometr...
متن کاملMedian graphs , the remoteness function , periphery transversals , and geodetic number two ∗
A periphery transversal of a median graph G is introduced as a set of vertices that meets all the peripheral subgraphs of G. Using this concept, median graphs with geodetic number 2 are characterized in two ways. They are precisely the median graphs that contain a periphery transversal of order 2 as well as the median graphs for which there exists a profile such that the remoteness function is ...
متن کاملThe t-median function on graphs
Amedian of a sequence π = x1, x2, . . . , xk of elements of a finite metric space (X, d) is an element x for which ∑k i=1 d(x, xi) is minimum. The function M with domain the set of all finite sequences on X and defined by M(π) = {x : x is a median of π} is called the median function on X, and is one of the most studied consensus functions. Based on previous characterizations of median sets M(π)...
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The average distance of a vertex $v$ of a connected graph $G$is the arithmetic mean of the distances from $v$ to allother vertices of $G$. The proximity $pi(G)$ and the remoteness $rho(G)$of $G$ are defined as the minimum and maximum averagedistance of the vertices of $G$. In this paper we investigate the difference between proximity or remoteness and the classical distanceparameters diameter a...
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Let e be an edge of a median graph G which is contained in exactly one 4-cycle. Then it is proved that G n e is a median graph. The converse holds as well provided that e is not contained is a subgraph isomorphic to the 3-cube minus a vertex. These results are used to give several characterizations of median grid graphs. (Grid graphs are subgraphs of complete grids, i.e. of the Cartesian produc...
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ژورنال
عنوان ژورنال: Discrete Applied Mathematics
سال: 2009
ISSN: 0166-218X
DOI: 10.1016/j.dam.2009.07.007