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In this paper, we derive a formula to express the maximum number of non-intersecting diagonals of arbitrary length that can be drawn in n x n square arrays, where n is a multiple of l+1., Comment: 14 pages

Let $S=(G, \sigma)$ be a signed graph where $G=(V, E)$ is a graph called the underlying graph of $S$ and $\sigma:E(G) \rightarrow \{+,~-\}$. Let $f:V(G) \rightarrow \{1,2,\dots,|V(G)|\}$ such that $\sigma(uv)=+$ if and only if $f(u)$ and $f(v)$ are of same parity and $\sigma(uv)=-$ if and only if $f(u)$ and $f(v)$ are of opposite parity. Under $f$ we get a signed graph $G_f$ denoted as $S$, which is a parity signed graph. In this paper, we initiate the study of parity labeling in signed graphs and we define and find `rna' number denoted as $\sigma^-(S)$ for some classes of signed graphs. We also characterize some signed graphs which are parity signed graphs. Some directions for further research are also suggested., Comment: 10 pages, 1 figure

The COVID-19 is the current widespread health disaster. It has speedily spread all over the world causing a massive impact on the health, environmental, social and economic condition of the total world's population. Enormous actions undertaken worldwide to minimize the expansion of this deadly contagion by testing at a large scale, quarantining the suspected people, upholding lockdowns and restricting social gatherings. The transportation sector has been one amid the leading sufferers of Coronavirus. Airlines, railways, and the public transport sector are badly hit due to this coronavirus outbreak. In this paper, we studied the effect of Coronavirus on the various transport sectors all over the world, taking into consideration the worldwide scenario and India's condition as well. Further, this paper analyses the possible ways and measures regarding how the transport services are dealing with this pandemic.