175 research outputs found
A Note on the Sparing Number of the Sieve Graphs of Certain Graphs
Let denote the set of all non-negative integers and
be its power set. An integer additive set-indexer
(IASI) of a given graph is an injective function such that the induced function defined by is also
injective. An IASI of a graph is said to be a weak IASI of if
for all . A graph which admits a
weak IASI may be called a weak IASI graph. The sparing number of a graph is
the minimum number of edges with singleton set-labels required for a graph
to admit a weak IASI. In this paper, we introduce the notion of -sieve
graphs of a given graph and study their sparing numbers.Comment: 9 pages, 3 figures, Publishe
A Note on the Sparing Number of Graphs
An integer additive set-indexer is defined as an injective function
such that the induced function defined by is also
injective. An IASI is said to be a weak IASI if
for all . A graph which admits a
weak IASI may be called a weak IASI graph. The set-indexing number of an
element of a graph , a vertex or an edge, is the cardinality of its
set-labels. The sparing number of a graph is the minimum number of edges
with singleton set-labels, required for a graph to admit a weak IASI. In
this paper, we study the sparing number of certain graphs and the relation of
sparing number with some other parameters like matching number, chromatic
number, covering number, independence number etc.Comment: 10 pages, 10 figures, submitte
On the Sparing Number of Certain Graph Structures
An integer additive set-indexer is defined as an injective function
such that the induced function defined by is also
injective. An IASI is said to be a weak IASI if
for all . A graph which admits a
weak IASI may be called a weak IASI graph. The set-indexing number of an
element of a graph , a vertex or an edge, is the cardinality of its
set-labels. A mono-indexed element of a graph is an element of which has
the set-indexing number . The Sparing number of a graph is the minimum
number of mono-indexed edges required for a graph to admit a weak IASI. In
this paper, we introduce the notion of conjoined graphs, entwined graphs and
floral graphs and study further about the sparing number of various finite
graph operations as extensions to our earlier studies and provide some useful
results on these types of graph structures.Comment: 12 pages, 5 figures. arXiv admin note: text overlap with
arXiv:1310.609
Weak Integer Additive Set-Indexers of Certain Graph Products
An integer additive set-indexer is defined as an injective function
such that the induced function defined by is also
injective, where is the sumset of and . If , then is said to be a -uniform integer additive
set-indexers. An integer additive set-indexer is said to be a weak integer
additive set-indexer if . We
have some characteristics of the graphs which admit weak integer additive
set-indexers. We already have some results on the admissibility of weak integer
additive set-indexer by certain graphs and finite graph operations. In this
paper, we study further characteristics of certain graph products like
cartesian product and corona of two weak IASI graphs and their admissibility of
weak integer additive set-indexers and provide some useful results on these
types of set-indexers.Comment: 7 pages, arXiv admin note: text overlap with arXiv:1310.6091,
arXiv:1311.0345, submitte
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
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