‎let $g=(v(g),e(g))$ be a graph‎, ‎$gamma_t(g)$. let $ooir(g)$ be the total domination and oo-irredundance number of $g$‎, ‎respectively‎. ‎a total dominating set $s$ of $g$ is called a $textit{total perfect code}$ if every vertex in $v(g)$ is adjacent to exactly one vertex of $s$‎. ‎in this paper‎, ‎we show that if $g$ has a total perfect code‎, ‎then $gamma_t(g)=ooir(g)$‎. ‎as a consequence, ...

the performance of msu-s and its forms modified with phosphotungstic acid (hpw) and nickel (ni) for the desulfurization and denitrogenation of model diesel fuel were studied. according to the results of the characteristic tests (n2 adsorption-desorption, xrd, sem, and nh3-tpd), heteropoly acid incorporation causes higher acidity along with a negligible loss of structural aspects, while ni impre...

Expressions for the Zagreb indices and coindices of the total graph, semi-total point graph and of semi-total line graph of subdivision graphs in terms of the parameters of the parent graph are obtained, thus generalizing earlier existing results.