Let G = (V, E) be a graph and let k ∈ Z +. A total k-subdominating function is a function f : V → {−1, 1} such that for at least k vertices v of G, the sum of the function values of f in the open neighborhood of v is positive. The total k-subdomination number of G is the minimum value of f (V) over all total k-subdominating functions f of G where f (V) denotes the sum of the function values assigned to the vertices under f. In this paper, we present a cubic time algorithm to compute the total k-subdomination number of a tree and also show that the associated decision problem is NP-complete for general graphs.
The objective of this work was to determine the effect of visibility-related factors and some environmental and human factors on the severity of pedestrian-vehicle crashes. It was hypothesized that decreasing visibility, contributed to by factors such as lighting, number of lanes, speed limit, and weather, are associated with an increase in injury severity. Some of the key results of the final model indicate that higher speed limits, less light conditions, and no traffic controls were significantly correlated with increased pedestrian injury severity when roadway visibility factors were under consideration. Dusk and dark with or without lighting were found to be factors correlated with increased pedestrian injury severity, while inclement weather was found to be correlated with lower pedestrian injury severity when environmental visibility-related factors were considered. Furthermore, a spatial autocorrelation revealed a high concentration of pedestrian–vehicle crashes in the Nashville and Memphis areas. This work is similar to prior works in their goal to study factors that affect pedestrian injury severity. While other models have looked at a large range of possible factors that may affect pedestrian injury severity, the model developed in this work focuses on visibility factors, environmental factors, and human-related factors. Another contribution is the data and modeling of the data. This study utilizes a dataset from Tennessee with more categories recorded for the visibility-related factors and applies a multinomial logistic regression model to the data.
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