Let G = V G, E G be a molecular graph, where V G and E G are the sets of vertices and edges. A topological index of a molecular graph is a numerical quantity which helps to predict the chemical/physical properties of the molecules. The Wiener, Wiener polarity, and the terminal Wiener indices are the distance-based topological indices. In this paper, we described a linear time algorithm that computes the Wiener index for acyclic graphs and extended this algorithm for (...) unicyclic graphs. The same algorithms are modified to compute the terminal Wiener index and the Wiener polarity index. All these algorithms compute the indices in time O n. (shrink)

Various cell types cooperate to create a highly organized and dynamic micro-environmental niche in the bone marrow. Over the past several years, the field has increasingly recognized the critical roles of the interplay between bone marrow environment and hematopoietic cells in normal and deranged hematopoiesis. These advances rely on several new technologies that have allowed us to characterize the identity and roles of these niches in great detail. Here, we review the progress of the last several years, list some of (...) the outstanding questions in the field and propose ways to target the diseased environment to better treat hematologic diseases. Understanding the extrinsic regulation by the niche will help boost hematopoiesis for regenerative medicine. Based on natural development of hematologic malignancies, we propose that combinatory targeting the niche and hematopoietic intrinsic mechanisms in early stages of hematopoietic malignancies may help eliminate minimal residual disease and have the highest efficacy. The bone marrow is the home for blood-forming hematopoietic stem and progenitor cells. Normal generation of blood and immune cells depends on highly regulated interactions between these stem and progenitor cells with their surrounding environment. Emerging evidence suggests that therapeutic interventions directed at these cellular interdependencies can help boost hematopoiesis and eradicate malignant hematopoietic cells. (shrink)