In memory of the outstanding theoretical chemist Nenad Trinajstić, Furtula introduced a new distance-based molecular structure descriptor "Trinajstić index" in chemical graph theory. In this paper, we propose the general Trinajstić index, and give the calculation formula of the general Trinajstić index for double-star graphs, double brooms, Kragujevac trees, firefly graphs and wheel graphs. As an application, we calculate the general Trinajstić index for some hydrocarbons.

The conditional matching preclusion number of a graph G , denoted by m p 1 G , is the minimum number of edges whose deletion results in the graph with no isolated vertices that has neither perfect matching nor almost-perfect matching. In this paper, we first give some sharp upper and lower bounds of conditional matching preclusion number. Next, the graphs with large and small conditional matching preclusion numbers are characterized, respectively. In the end, we investigate some extremal problems on conditional matching preclusion number.