Topological subsystem codes from graphs and hypergraphs

Use of Structure Codes (Counts) for Computing Topological Indices of Carbon Nanotubes: Sadhana (Sd) Index of Phenylenes and its Hexagonal Squeezes

Structural codes vis-a-vis structural counts, like polynomials of a molecular graph, are important in computing graph-theoretical descriptors which are commonly known as topological indices. These indices are most important for characterizing carbon nanotubes (CNTs). In this paper we have computed Sadhana index (Sd) for phenylenes and their hexagonal squeezes using structural codes (counts). Sa...

Extremal Hypergraphs for Ryser’s Conjecture I: Connectedness of Line Graphs of Bipartite Graphs

Ryser’s Conjecture states that any r-partite r-uniform hypergraph has a vertex cover of size at most r− 1 times the size of the largest matching. For r = 2, the conjecture is simply König’s Theorem. It has also been proven for r = 3 by Aharoni using a beautiful topological argument. This paper is the first part of the proof of a characterization of those 3-uniform hypergraphs for which Aharoni’...

CATEGORY OF (POM)L-FUZZY GRAPHS AND HYPERGRAPHS

In this note by considering a complete lattice L, we define thenotion of an L-Fuzzy hyperrelation on a given non-empty set X. Then wedefine the concepts of (POM)L-Fuzzy graph, hypergraph and subhypergroupand obtain some related results. In particular we construct the categories ofthe above mentioned notions, and give a (full and faithful) functor form thecategory of (POM)L-Fuzzy subhypergroups ...

Ryan Martin

The focus of my research is extremal graph theory and random combinatorial structures. I have also worked in a variety of other areas, including intersecting hypergraphs, the theory of positional games and Ramsey theory. Combinatorics, and particularly graph theory, has a wide variety of applications. My own research in the edit distance of graphs has applications in biology and computer scienc...

Topological subsystem codes