Perfect Neighbor Sets in Graphs

Hastürk, Umur
Tural, Mustafa Kemal


Varli, Hanife; Pamuk, Mehmetcik; Kosta, Neza Mramor (2018-01-01)
We study perfect discrete Morse functions on closed, connected, oriented n-dimensional manifolds. We show how to compose such functions on connected sums of manifolds of arbitrary dimensions and how to decompose them on connected sums of closed oriented surfaces.
Perfect discrete morse functions on connected sums
Varlı, Hanife; Pamuk, Mehmetcik; Kosta, Neza Mramor; Department of Mathematics (2017)
Let $K$ be a finite, regular cell complex and $f$ be a real valued function on $K$. Then $f$ is called a textit{discrete Morse function} if for all $p$-cell $sigma in K$, the following conditions hold: begin{align*} displaystyle n_{1}=# {tau > sigma mid f(tau)leq f(sigma)} leq 1, \ n_{2}=# {nu < sigma mid f(nu)geq f(sigma)}leq 1. end{align*} A $p$-cell $sigma$ is called a textit{critical $p$-cell} if $n_{1}=n_{2}=0$. A discrete Morse function $f$ is called a textit{perfect discrete Morse function} if the nu...
Perfect Discrete Morse Functions On Connected Sums
Pamuk, Mehmetcik (2017-07-01)
In this talk, we study perfect discrete Morse functions on closed oriented n-dimensional manifolds. First, we show how to compose such functions on connected sums of manifolds. Then we discuss how to decompose such functions, particularly in dimensions 2 and 3.
Maximal green sequences of skew-symmetrizable 3 x 3 matrices
Seven, Ahmet İrfan (2014-01-01)
Maximal green sequences are particular sequences of mutations of skew-symmetrizable matrices which were introduced by Keller in the context of quantum dilogarithm identities and independently by Cecotti-Cordova-Vafa in the context of supersymmetric gauge theory. In this paper we study maximal green sequences of skew-symmetrizable 3 x 3 matrices. We show that such a matrix with a mutation-cyclic diagram does not have any maximal green sequence. We also obtain some basic properties of maximal green sequences ...
Prime graphs of solvable groups
Ulvi , Muhammed İkbal; Ercan, Gülin; Department of Electrical and Electronics Engineering (2020-8)
If $G$ is a finite group, its prime graph $Gamma_G$ is constructed as follows: the vertices are the primes dividing the order of $G$, two vertices $p$ and $q$ are joined by an edge if and only if $G$ contains an element of order $pq$. This thesis is mainly a survey that gives some important results on the prime graphs of solvable groups by presenting their proofs in full detail.
Citation Formats
U. Hastürk and M. K. Tural, “Perfect Neighbor Sets in Graphs,” 2019, Accessed: 00, 2021. [Online]. Available: