For a rooted graph G, let EVb(G; p) be the expected number of vertices reachable from the root when each edge has an independent probability p of operating successfully. We determine the expected value of EVb(G; p) for random trees, and include a connection to unrooted trees. We also consider rooted digraphs, computing the expected value of a random orientation of a rooted graph G in terms of E...

For a rooted graph G, let EV (G; p) be the expected number of vertices reachable from the root when each edge has an independent probability p of operating successfully. We examine combinatorial properties of this polynomial, proving that G is k-edge connected iff EV ′(G; 1) = · · · = EV k−1(G; 1) = 0. We find bounds on the first and second derivatives of EV (G; p); applications yield character...

the vast majority of mandibular second molars have two roots with three root canals; however, variations in molar root canal anatomy are not uncommon. to the best of our knowledge, four rooted mandibular second molar with three mesial roots and one distal root has never been reported. herein, we present the endodontic management of a four rooted mandibular second molar tooth, diagnosed with the...

Introduction Age estimation holds significant importance within the realm of forensic science, serving as a crucial tool for various purposes such validating birth certificates, aiding immigration processes, and determining eligibility retirement benefits. Additionally, age carries implications in situations involving human trafficking, offering insights into matters legal culpability, adult cl...

OBJECTIVE The purpose of this study was to investigate the root/number of roots and morphology of mandibular premolars and molars in a Korean population, and to evaluate the prevalence of three-rooted mandibular first molars having distolingual (DL) roots, three-rooted mandibular second molars, and C-shaped roots in mandibular second molars. METHODS Serial axial cone-beam computed tomography ...

For finite q, we classify the countable, descendant-homogeneous digraphs in which the descendant set of any vertex is a q-valent tree. We also give conditions on a rooted digraph Γ which allow us to construct a countable descendant-homogeneous digraph in which the descendant set of any vertex is isomorphic to Γ. 2010 Mathematics Subject Classification: 05C20, 05C38, 20B27