146 research outputs found
A Study on Edge-Set Graphs of Certain Graphs
Let be a simple connected graph, with In this
paper, we define an edge-set graph constructed from the graph
such that any vertex of corresponds to the -th
-element subset of and any two vertices of
are adjacent if and only if there is at least one edge in the
edge-subset corresponding to which is adjacent to at least one edge
in the edge-subset corresponding to where are positive
integers. It can be noted that the edge-set graph of a graph
id dependent on both the structure of as well as the number of edges
We also discuss the characteristics and properties of the edge-set
graphs corresponding to certain standard graphs.Comment: 10 pages, 2 figure
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
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