10,648 research outputs found
A Study on Integer Additive Set-Graceful Graphs
A set-labeling of a graph is an injective function , where is a finite set and a set-indexer of is a
set-labeling such that the induced function defined by
for every is also injective. An integer additive set-labeling is
an injective function ,
is the set of all non-negative integers and an integer additive
set-indexer is an integer additive set-labeling such that the induced function
defined by is also injective. In this paper, we extend the concepts of set-graceful
labeling to integer additive set-labelings of graphs and provide some results
on them.Comment: 11 pages, submitted to JARP
A Study on Integer Additive Set-Valuations of Signed Graphs
Let denote the set of all non-negative integers and \cP(\N) be its
power set. An integer additive set-labeling (IASL) of a graph is an
injective set-valued function f:V(G)\to \cP(\N)-\{\emptyset\} such that the
induced function f^+:E(G) \to \cP(\N)-\{\emptyset\} is defined by , where is the sumset of and . A graph
which admits an IASL is usually called an IASL-graph. An IASL of a graph
is said to be an integer additive set-indexer (IASI) of if the
associated function is also injective. In this paper, we define the
notion of integer additive set-labeling of signed graphs and discuss certain
properties of signed graphs which admits certain types of integer additive
set-labelings.Comment: 12 pages, Carpathian Mathematical Publications, Vol. 8, Issue 2,
2015, 12 page
A Study on Topological Integer Additive Set-Labeling of Graphs
A set-labeling of a graph is an injective function , where is a finite set and a set-indexer of is a
set-labeling such that the induced function defined by
for every is also injective. Let be a graph and let be a
non-empty set. A set-indexer is called a topological
set-labeling of if is a topology of . An integer additive
set-labeling is an injective function ,
whose associated function is defined by
, where is the set of all
non-negative integers and is its power set. An
integer additive set-indexer is an integer additive set-labeling such that the
induced function defined by is also injective. In this paper, we extend the concepts of
topological set-labeling of graphs to topological integer additive set-labeling
of graphs.Comment: 16 pages, 7 figures, Accepted for publication. arXiv admin note: text
overlap with arXiv:1403.398
A Characterisation of Weak Integer Additive Set-Indexers of Graphs
An integer additive set-indexer is defined as an injective function
such that the induced function defined by is also
injective. An integer additive set-indexer is said to be -uniform if
for all . An integer additive set-indexer is said
to be a weak integer additive set-indexer if for
all . In this paper, we study the characteristics of certain
graphs and graph classes which admit weak integer additive set-indexers.Comment: 12pages, 4 figures, arXiv admin note: text overlap with
arXiv:1311.085
Strong Integer Additive Set-valued Graphs: A Creative Review
For a non-empty ground set , finite or infinite, the {\em set-valuation}
or {\em set-labeling} of a given graph is an injective function , where is the power set of the set . A
set-indexer of a graph is an injective set-valued function such that the function defined by for
every is also injective., where is a binary operation on
sets. An integer additive set-indexer is defined as an injective function
such that the induced function
defined by is
also injective, where is the set of all non-negative integers
and is its power set. An IASI is said to be a
strong IASI if for every pair of adjacent vertices
in . In this paper, we critically and creatively review the concepts
and properties of strong integer additive set-valued graphs.Comment: 13 pages, Published. arXiv admin note: text overlap with
arXiv:1407.4677, arXiv:1405.4788, arXiv:1310.626
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