21 research outputs found
Alliance Partition Number in Graphs
Ars Combinatoria, 103 (2012), pp. 519-529 (accepted 2007)
Metric dimension and zero forcing number of two families of line graphs
summary:Zero forcing number has recently become an interesting graph parameter studied in its own right since its introduction by the “AIM Minimum Rank–Special Graphs Work Group”, whereas metric dimension is a well-known graph parameter. We investigate the metric dimension and the zero forcing number of some line graphs by first determining the metric dimension and the zero forcing number of the line graphs of wheel graphs and the bouquet of circles. We prove that for a simple and connected graph . Further, we show that when is a tree or when contains a Hamiltonian path and has a certain number of edges. We compare the metric dimension with the zero forcing number of a line graph by demonstrating a couple of inequalities between the two parameters. We end by stating some open problems
Domination in Functigraphs
Let and be disjoint copies of a graph , and let be a function. Then a \emph{functigraph}
has the vertex set and the edge set . A functigraph is a
generalization of a \emph{permutation graph} (also known as a \emph{generalized
prism}) in the sense of Chartrand and Harary. In this paper, we study
domination in functigraphs. Let denote the domination number of
. It is readily seen that . We
investigate for graphs generally, and for cycles in great detail, the functions
which achieve the upper and lower bounds, as well as the realization of the
intermediate values.Comment: 18 pages, 8 figure
On Metric Dimension of Functigraphs
The \emph{metric dimension} of a graph , denoted by , is the
minimum number of vertices such that each vertex is uniquely determined by its
distances to the chosen vertices. Let and be disjoint copies of a
graph and let be a function. Then a
\emph{functigraph} has the vertex set
and the edge set . We study how
metric dimension behaves in passing from to by first showing that
, if is a connected graph of order
and is any function. We further investigate the metric dimension of
functigraphs on complete graphs and on cycles.Comment: 10 pages, 7 figure
Global Alliance Partition in Trees
J. Combin. Math. Combin Comput. 66 (2008), 161-16
Closed 3-stop Center and Periphery in Graphs
Acta Mathematica Sinica, English Series Vol 28 No. 3 (2012)The article of record as published may be located at http://dx.doi.org/10.1007/s10114-011-0187-
Closed k-stop distance in graphs
Discussions Mathematicae Graph Theory 31 (2011) 533 – 545 bibte