3,077 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
On certain topological indices of the derived graphs of subdivision graphs
The derived graph [G]† of a graph G is the graph having the same vertex set as G, with two vertices of [G]† being adjacent if and only if their distance in G is two. Topological indices are valuable in the study of QSAR/QSPR. There are numerous applications of graph theory in the field of structural chemistry. In this paper, we compute generalized Randi´c, general Zagreb, general sum-connectivity, ABC, GA, ABC4, and GA5 indices of the derived graphs of subdivision graphs.Publisher's Versio
Atom-bond-connectivity index of certain graphs
The ABC index is one of the most applicable topological graph indices and several properties of it has been studied already due to its extensive chemical applications. Several variants of it have also been defined and used for several reasons. In this paper, we calculate the atom-bond connectivity index of some derived graphs such as double graphs, subdivision graphs and complements of some standard graphs.Publisher's Versio
Topological minors of cover graphs and dimension
We show that posets of bounded height whose cover graphs exclude a fixed
graph as a topological minor have bounded dimension. This result was already
proven by Walczak. However, our argument is entirely combinatorial and does not
rely on structural decomposition theorems. Given a poset with large dimension
but bounded height, we directly find a large clique subdivision in its cover
graph. Therefore, our proof is accessible to readers not familiar with
topological graph theory, and it allows us to provide explicit upper bounds on
the dimension. With the introduced tools we show a second result that is
supporting a conjectured generalization of the previous result. We prove that
-free posets whose cover graphs exclude a fixed graph as a topological
minor contain only standard examples of size bounded in terms of .Comment: revised versio
Feynman Diagrams of Generalized Matrix Models and the Associated Manifolds in Dimension 4
The problem of constructing a quantum theory of gravity has been tackled with
very different strategies, most of which relying on the interplay between ideas
from physics and from advanced mathematics. On the mathematical side, a central
role is played by combinatorial topology, often used to recover the space-time
manifold from the other structures involved. An extremely attractive
possibility is that of encoding all possible space-times as specific Feynman
diagrams of a suitable field theory. In this work we analyze how exactly one
can associate combinatorial 4-manifolds to the Feynman diagrams of certain
tensor theories.Comment: 25 pages, 10 figures. Minor cange
Exponential fraction index of certain graphs
Topological indices play a great role in Mathematical chemistry. Many graph theorists as well as chemists attracted towards these molecular descriptors. The aim of this paper is to introduce and investigate the Exponential Fraction index (a degree based Topological index). It is defined as follows. EF(G) = Σ uv∈E(G) edu/dv . Here du and dv are the maximum and minimum degree respectively. In this paper, we calculate the Exponential Fraction index of double graphs, subdivision graphs and complements of some standard graphs. Also we compute the index for chemical structures Graphene and Carbon nanocones.Publisher's Versio
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