A Study on Non-Performing Assets (NPA) of Selected Private Sector Banks in India

The banking industry is critical to the success of any economy since it satisfies societal requirements. A bank is a financial entity that provides its clients with a variety of banking and other financial services. India's banking industry has been grappling with mounting non-performing assets. The rise of Non-Performing Assets has a significant impact on a bank's profitability. This research was undertaken in order to analyze the non-performing assets of a sample of chosen private sector banks in India. For that purpose, the researcher chose the top four private sector banks, namely HDFC bank, ICICI bank, Axis bank, and Indusland bank, based on their net sales from 2016-17 to 2020-21. To analyze non-performing assets in a selected private sector in India, gross non-performing assets (NPAs), net non-performing assets (NPAs), and net profit ratios were chosen. To test the hypothesis, the researcher employed a one-way ANOVA with a significance level of 5%. The study's primary conclusions include that HDFC bank's average GNPA and average NNPA are the lowest in the industry, while ICICI banks are the highest.

On Ramsey Numbers of Path Versus Wheel-Like Graphs

The study of classical Ramsey numbers R(m, n) shows little progress in the last two decades. Only nine classical Ramsey numbers are known. This difficulty of finding the classical Ramsey numbers has inspired many people to study generalizations of classical Ramsey number. One of them is to determine Ramsey number R(G, H) for general graphs G and H (not necessarily complete). One of the most general results on graph Ramsey numbers is the establish- ment of a general lower bound by Chv ́atal and Harary [17] which is formulated as: R(G, H) ≥ (χ(H) − 1)(c(G) − 1) + 1, where G is a graph having no isolated vertices, χ(H) is the chromatic number of H and c(G) denotes the cardinality of large con- nected component of G. Recently, Surahmat and Tomescu [41] studied the Ramsey number of a combina- tion of path P n versus Jahangir graph J 2,m . They proved that R(P n , J 2,m ) = n+m−1 for m ≥ 3 and n ≥ (4m − 1)(m − 1) + 1. Furthermore, they determined that R(P 4 , J 2,2 ) = 6 and R(P n , J 2,2 ) = n + 1 for n ≥ 5. This dissertation studies the determination of Ramsey number for a combination of path P n and a wheel-like graph. What we mean by wheel-like graph, is a graph obtained from a wheel by a graph operation such as deletion or subdivision of the spoke edges. The classes of wheel-like graphs which we consider are Jahangir graph, generalized Jahangir graph and beaded wheel. First of all we evaluate the Ramsey number for path P n with respect to Jahangir graph J 2,m . We improve the result of Surahmat and Tomescu for m = 3, 4, 5 with n ≥ 2m + 1. Also, we determine the Ramsey number for disjoint union of k identical copies of path P n versus Jahangir graph J 2,m for m ≥ 2. Moreover, we determine the Ramsey number of path P n versus generalized Ja- hangir graph J s,m for different values of s, m and n. We also, evaluate the Ramsey number for combination of disjoint union of t identical copies of path versus general- ized Jahangir graph J s,m for even s ≥ 2 and m ≥ 3. At the end, we find the Ramsey number of path versus beaded wheel BW 2,m , i.e. R(P n , BW 2,m ) = 2n − 1 or 2n if m ≥ 3 is even or odd, respectively, provided n ≥ 2m 2 − 5m + 4.