208,624 research outputs found
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
Integer symmetric matrices having all their eigenvalues in the interval [-2,2]
We completely describe all integer symmetric matrices that have all their
eigenvalues in the interval [-2,2]. Along the way we classify all signed
graphs, and then all charged signed graphs, having all their eigenvalues in
this same interval. We then classify subsets of the above for which the integer
symmetric matrices, signed graphs and charged signed graphs have all their
eigenvalues in the open interval (-2,2).Comment: 33 pages, 18 figure
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
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