84 research outputs found
Topological Integer Additive Set-Sequential Graphs
Let denote the set of all non-negative integers and be any
non-empty subset of . Denote the power set of by
. An integer additive set-labeling (IASL) of a graph is an
injective set-valued function such that the induced
function is defined by ,
where is the sumset of and . If the associated
set-valued edge function is also injective, then such an IASL is called
an integer additive set-indexer (IASI). An IASL is said to be a topological
IASL (TIASL) if is a topology of the ground set
. An IASL is said to be an integer additive set-sequential labeling (IASSL)
if . An IASL of a given
graph is said to be a topological integer additive set-sequential labeling
of , if it is a topological integer additive set-labeling as well as an
integer additive set-sequential labeling of . In this paper, we study the
conditions required for a graph to admit this type of IASL and propose some
important characteristics of the graphs which admit this type of IASLs.Comment: 10 pages, 2 figures. arXiv admin note: text overlap with
arXiv:1506.0124
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