87 research outputs found
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
On Integer Additive Set-Indexers of Graphs
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
the set of all subsets of and is the symmetric difference of sets.
An integer additive set-indexer is defined as an injective function
such that the induced function defined by is also
injective. A graph which admits an IASI is called an IASI graph. An IASI
is said to be a {\em weak IASI} if and an
IASI is said to be a {\em strong IASI} if for all
. In this paper, we study about certain characteristics of inter
additive set-indexers.Comment: 12 pages. arXiv admin note: text overlap with arXiv:1312.7674 To
Appear in Int. J. Math. Sci.& Engg. Appl. in March 201
A Creative Review on Integer Additive Set-Valued Graphs
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.
In this paper, we critically and creatively review the concepts and properties
of integer additive set-valued graphs.Comment: 14 pages, submitted. arXiv admin note: text overlap with
arXiv:1312.7672, arXiv:1312.767
Further Studies on the Sparing Number of Graphs
Let denote the set of all non-negative integers and
be its power set. An integer additive set-indexer
is an injective function such that the
induced function defined by is also injective, where is the sum set of and
. If , then is said to be a -uniform
integer additive set-indexer. An integer additive set-indexer is said to be
a weak integer additive set-indexer if . In this paper, we study the admissibility of weak integer additive
set-indexer by certain graphs and graph operations.Comment: 10 Pages, Submitted. arXiv admin note: substantial text overlap with
arXiv:1310.609
Associated Graphs of Certain Arithmetic IASI Graphs
An integer additive set-indexer is defined as an injective function
such that the induced function defined by is also
injective. A graph which admits an IASI is called an IASI graph. An
arithmetic integer additive set-indexer is an integer additive set-indexer ,
under which the set-labels of all elements of a given graph are arithmetic
progressions. In this paper, we discuss about admissibility of arithmetic
integer additive set-indexers by certain associated graphs of the given graph
, like line graph, total graph, etc.Comment: 11 pages. arXiv admin note: text overlap with arXiv:1312.7674,
arXiv:1312.767
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