Eccentric connectivity index

The eccentric connectivity index $\xi^c$ is a novel distance--based molecular structure descriptor that was recently used for mathematical modeling of biological activities of diverse nature. It is defined as $\xi^c (G) = \sum_{v \in V (G)} deg (v) \cdot \epsilon (v)$\,, where $deg (v)$ and $\epsilon (v)$ denote the vertex degree and eccentricity of $v$\,, respectively. We survey some mathematical properties of this index and furthermore support the use of eccentric connectivity index as topological structure descriptor. We present the extremal trees and unicyclic graphs with maximum and minimum eccentric connectivity index subject to the certain graph constraints. Sharp lower and asymptotic upper bound for all graphs are given and various connections with other important graph invariants are established. In addition, we present explicit formulae for the values of eccentric connectivity index for several families of composite graphs and designed a linear algorithm for calculating the eccentric connectivity index of trees. Some open problems and related indices for further study are also listed.Comment: 25 pages, 5 figure

Modeling Site Specific Heterogeneity in an On-Site Stratified Random Sample of Recreational Demand

Using estimation of demand for the George Washington/Jefferson National Forest as a case study, it is shown that in a stratified/clustered on-site sample, latent heterogeneity needs to be accounted for twice: first to account for dispersion in the data caused by unobservability of the process that results in low and high frequency visitors in the population, and second to capture unobservable heterogeneity among individuals surveyed at different sites according to a stratified random sample (site specific effects). It is shown that both of the parameters capturing latent heterogeneity are statistically significant. It is therefore claimed in this paper, that the model accounting for site-specific effects is superior to the model without such effects. Goodness of fit statistics show that our empirical model is superior to models that do not account for latent heterogeneity for the second time. The price coefficient for the travel cost variable changes across model resulting in differences in consumer surplus measures. The expected mean also changes across different models. This information is of importance to the USDA Forest Service for the purpose of consumer surplus calculations and projections for budget allocation and resource utilization.Recreational Demand models, Clustering, Subject-specific effects, Truncated Stratified Negative Binomial Model, Overdispersion, Environmental Economics and Policy,

On a lower bound for the eccentric connectivity index of graphs

The eccentric connectivity index of a graph $G$, denoted by $\xi^{c}(G)$, defined as $\xi^{c}(G)$ = $\sum_{v \in V(G)}\epsilon(v) \cdot d(v)$, where $\epsilon(v)$ and $d(v)$ denotes the eccentricity and degree of a vertex $v$ in a graph $G$, respectively. The volcano graph $V_{n,d}$ is a graph obtained from a path $P_{d+1}$ and a set $S$ of $n-d-1$ vertices, by joining each vertex in $S$ to a central vertex or vertices of $P_{d+1}$. In (A lower bound on the eccentric connectivity index of a graph, Discrete Applied Math., 160, 248 to 258, (2012)), Morgan et al. proved that $\xi^{c}(G) \geq \xi^{c}(V_{n,d})$ for any graph of order $n$ and diameter $d \geq 3$. In this paper, we present a short and simple proof of this result by considering the adjacency of vertices in graphs.Comment: 9 pages, CALDAM 2018 conference proceeding pape

An Optimal Rule for Switching over to Renewable fuels with Lower Price Volatility: A Case of Jump Diffusion Process

This study investigates the optimal switching boundary to a renewable fuel when oil prices exhibit continuous random fluctuations along with occasional discontinuous jumps. In this paper, oil prices are modeled to follow jump diffusion processes. A completeness result is derived. Given that the market is complete the value of a contingent claim is risk neutral expectation of the discounted pay off process. Using the contingent claim analysis of investment under uncertainty, the Hamilton-Jacobi-Bellman (HJB) equation is derived for finding value function and optimal switching boundary. We get a mixed differential-difference equation which would be solved using numerical methods.Demand and Price Analysis, Resource /Energy Economics and Policy,

Minsung Kim, cello and Siu Yan Luk, piano, May 6, 2018

This is the concert program of the Minsung Kim, cello and Siu Yan Luk, piano performance on Sunday, May 6, 2018 at 6:30 p.m., at the Marshall Room, 855 Commonwealth Avenue. Works performed were 12 Variations in G major on "See The Conqu'ring Hero Comes" from Handel's Judas Maccabaeus, WoO 45 by Ludwig van Beethoven, Suite for Solo Cello by Gaspar Cassadó, and Sonata in G minor for Cello and Piano, Op. 19 by Sergei Rachmaninoff. Digitization for Boston University Concert Programs was supported by the Boston University Humanities Library Endowed Fund