This seminar takes place usually on Fridays, at a suitable time and is meant for talks by young Assamese mathematicians (PhD Students, Postdocs, and young faculty members). By Assamese, we mean anyone residing/working in Assam now or residing/working in Assam in the past. If you wish to attend or give a talk in the seminar please email me ([email protected]) or Parama Dutta ([email protected]).

Check the FAQs.

All the talks will be over Zoom and the meeting details will be emailed to the registered participants.

**Some aspects of $\Gamma_2$ graph over some of the finite commutative rings**

**Anurag Baruah (Gauhati University)**

**14 August 2020 (8 pm IST)**

**Abstract**: Among graphs associated to a ring, Zero-divisor graph holds a special place as it reveals interesting relations between ring theory and graph theory. After the concept of zero-divisor graph was introduced by Beck in 1988, Anderson and Livingston modified this definition of zero divisor graph in 1999 by restricting the vertices to the non-zero zero divisors of the ring $R$. In 2008, Anderson and Badawi introduced the total graph $\Gamma (R)$ of a commutative ring $R$. Motivated by the significant results obtained from the structure of $\Gamma (R)$, Sengupta introduced a new type of graph over rings, involving both the operations of a ring in the adjacency conditions. Let $R$ be a ring then $\Gamma_2$ is an undirected graph $(V,E)$ in which $V = R \setminus {0}$ and for any $a, b \in V$, $ab \in E$ if and only if $a \neq b$ and either $a\cdot b = 0$ or $b \cdot a = 0$ or $a + b$ is a zero-divisor (including $0$). Here the general structure of this graph is dicussed for some of the finite commutative rings and other properties like connectedness, diameter, girth, chromatic number, completeness, eulerianity and planarity of these graphs are also determined.

*Please click on the title to see the abstract.*

**What is the Probability that an automorphism fixes a group element?** (*Parama Dutta*: 26 June 2020)

**Hypergeometric Series over Finite Fields** (*Arjun Singh Chetry*: 10 July 2020)

**Families of Congruences for Fractional Partition Functions Modulo Powers of Primes** (*Hirakjyoti Das*: 17 July 2020)

**Combinatorics of Stammering Tableaux** (*Bishal Deb*: 31 July 2020)

**An approach to construct Mathematical model through system of ordinary differential equation** (*Munmi Saikia*: 07 August 2020)

**When does the seminar take place?**

Usually on Fridays, the times change depending on the availability of the speaker.

**Who can attend?**

Everyone is welcome to attend, but you have to register to get the links to attend the seminars. You can register by sending an email to [email protected], mentioning your name and affiliation (if any).

**Who can give a talk?**

At the moment we are encouraging only PhD students, postdocs and young faculty members either from Assam or living in Assam to give talks. If you are interested in giving a talk, please send an email to [email protected] or [email protected]

**Will there be any certificate for attending?**

No.