On the General Sum-connectivity Index of Connected Graphs with Given Order and Girth

In this paper, we show that in the classof connected graphs $G$ of order $n\geq 3$ having girth at least equal to $k$, $3\leq k\leq n$, the unique graph $G$ having minimum general sum-connectivity index $\chi _{\alpha }(G)$ consists of $C_{k}$ and $n-k$ pendant vertices adjacent to a unique vertex of $C_{k}$, if -1\leq \alpha <0. This property does not hold for zeroth-order general Randi\' c index $^{0}R_{\alpha}(G)$

Safely Filling Gaps with Partial Solutions Common to All Solutions

Gap filling has emerged as a natural sub-problem of many de novo genome assembly projects. The gap filling problem generally asks for an s-t path in an assembly graph whose length matches the gap length estimate. Several methods have addressed it, but only few have focused on strategies for dealing with multiple gap filling solutions and for guaranteeing reliable results. Such strategies include reporting only unique solutions, or exhaustively enumerating all filling solutions and heuristically creating their consensus. Our main contribution is a new method for reliable gap filling: filling gaps with those sub-paths common to all gap filling solutions. We call these partial solutions safe, following the framework of (Tomescu and Medvedev, RECOMB 2016). We give an efficient safe algorithm running in O(dm) time and space, where d is the gap length estimate and m is the number of edges of the assembly graph. To show the benefits of this method, we implemented this algorithm for the problem of filling gaps in scaffolds. Our experimental results on bacterial and on conservative human assemblies show that, on average, our method can retrieve over 73 percent more safe and correct bases as compared to previous methods, with a similar precision.Peer reviewe

Random generation of essential directed acyclic graphs

Peer reviewe

Safe and Complete Contig Assembly Through Omnitigs

Peer reviewe