Kannan, Balakrishnan; Ram Kumar, r(Hindawi Publishing Corporation, October 18, 2012)
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Abstract:
A profile is a finite sequence of vertices of a graph. The set of all vertices of the graph which
minimises the sum of the distances to the vertices of the profile is the median of the profile. Any
subset of the vertex set such that it is the median of some profile is called a median set. The number
of median sets of a graph is defined to be the median number of the graph. In this paper, we identify
the median sets of various classes of graphs such as Kp − e, Kp,q forP > 2, and wheel graph and so
forth. The median numbers of these graphs and hypercubes are found out, and an upper bound for
the median number of even cycles is established.We also express the median number of a product
graph in terms of the median number of their factors.
Description:
International Scholarly Research Network
ISRN Discrete Mathematics
Volume 2012, Article ID 583671, 8 pages
doi:10.5402/2012/583671