Congregational Composition and Explanations for Racial Inequality Among Black Religious Affiliates

Prior research suggests that congregational characteristics are associated with the racial attitudes of Black churchgoers. This study examines the relationship between congregational diversity and beliefs about the Black/White socioeconomic gap among Black religious adherents. Drawing upon pooled data from the General Social Survey and the National Congregations Study, we fit binary logistic regression models to estimate the association between congregational diversity and the explanations of Black/White economic inequality among Black religious adherents. Findings from our study reveal that congregational diversity is one factor that accounts for intragroup differences in racial attitudes among Black religious affiliates. Relative to Blacks that attend religious services in overwhelmingly Black congregations, Blacks that attend religious services in congregations that are overwhelmingly White are significantly less likely to attribute Black/White socioeconomic gaps to a lack of educational opportunities. Our study demonstrates that congregational diversity is a source of intragroup variation in racial attitudes among Black religious affiliates, which may attenuate the ability of such congregations to bridge racial divisions.     

African American Adolescents’ Psychological Well-Being: The Impact of Parents’ Religious Socialization on Adolescents’ Religiosity

The dearth of research literature on the religious beliefs and practices of African American adolescents has led to increased empirical inquiry, yet a lack of research considers African American adolescents’ religious beliefs and practices as an important developmental milestone. This study explored how African American parents’ religious socialization affected youth religious experiences and served as a culturally specific strength-based asset that promotes psychological well-being. Our sample included a socioeconomically diverse sample of 154 African American families. Accounting for demographics, adolescents’ relationship and communication with God were found to be associated with a healthier psychological well-being. Additionally, parents’ religious socialization impacted the relationship between youths religious beliefs and practice and psychological well-being. Overall, results suggest that parents’ and adolescents’ religious beliefs can promote psychological well-being.     

Mosque-Based Social Support and Collective and Personal Self-Esteem Among Young Muslim American Adults

This study investigated the association between congregational relationships and personal and collective self-esteem among young Muslim American adults. Mosque-based emotional support and negative interactions with congregants were assessed in relation to personal and collective self-esteem. Data analysis was based on a sample of 231 respondents residing in southeast Michigan. Results indicated that receiving emotional support from congregants was associated with higher levels of collective self-esteem but was unassociated with personal self-esteem. Negative interaction with congregants was associated with personal self-esteem. Together, these findings indicate that mosque-based emotional support and negative interactions function differently for personal and collective self-esteem, which provides evidence that although personal and collective self-esteem are interrelated constructs, they are also conceptually discrete aspects self-evaluations.     

Dual class shares,board of directors’ effectiveness and firm’s market value: an empirical study

This study aims to identify whether a relationship exists between the controlling shareholders’ voting power and outside directors’ effectiveness in maximizing firms’ financial performance. We analyze a panel data with 3057 observations for the 2000–2012 period using a random effects model, logit and probit regressions, and the two-stage model of Heckman in the Brazilian stock market. Our findings show that firms whose controlling shareholders use dual class shares to leverage their voting power have less independence from the board and worse financial performance and market value. Further, the percentage of outside directors tends to be ineffective in increasing the firm’s value, and in changing the firm’s chief executive officer (CEO) when (1) the controlling shareholder’s voting power is leveraged, or (2) when the CEO assumes a position on the board of directors simultaneously. We interpreted that these results are in line with the arguments in favor of the existence of a new agency cost, which is related to the undue obedience of board members to authority, such as the largest controlling shareholder or the CEO in Brazilian listed firms.     

The Weight Function Lemma for graph pebbling

Graph pebbling is a network model for studying whether or not a given supply of discrete pebbles can satisfy a given demand via pebbling moves. A pebbling move across an edge of a graph takes two pebbles from one endpoint and places one pebble at the other endpoint; the other pebble is lost in transit as a toll. It has been shown that deciding whether a supply can meet a demand on a graph is NP-complete. The pebbling number of a graph is the smallest t such that every supply of t pebbles can satisfy every demand of one pebble byt a vertex. Deciding if the pebbling number is at most k is \(\Pi _2^\mathsf{P}\)-complete. In this paper we develop a tool, called the Weight Function Lemma, for computing upper bounds and sometimes exact values for pebbling numbers with the assistance of linear optimization. With this tool we are able to calculate the pebbling numbers of much larger graphs than in previous algorithms, and much more quickly as well. We also obtain results for many families of graphs, in many cases by hand, with much simpler and remarkably shorter proofs than given in previously existing arguments (certificates typically of size at most the number of vertices times the maximum degree), especially for highly symmetric graphs. Here we apply the Weight Function Lemma to several specific graphs, including the Petersen, Lemke, \(4\mathrm{th}\) weak Bruhat, and Lemke squared, as well as to a number of infinite families of graphs, such as trees, cycles, graph powers of cycles, cubes, and some generalized Petersen and Coxeter graphs. In doing so we partly answer a question of Pachter, et al., by computing the pebbling exponent of cycles to within an asymptotically small range. It is conceivable that this method yields an approximation algorithm for graph pebbling.     

Is there any polynomial upper bound for the universal labeling of graphs?

A universal labeling of a graph G is a labeling of the edge set in G such that in every orientation \(\ell \) of G for every two adjacent vertices v and u, the sum of incoming edges of v and u in the oriented graph are different from each other. The universal labeling number of a graph G is the minimum number k such that G has universal labeling from \(\{1,2,\ldots , k\}\) denoted it by \(\overrightarrow{\chi _{u}}(G) \). We have \(2\Delta (G)-2 \le \overrightarrow{\chi _{u}} (G)\le 2^{\Delta (G)}\), where \(\Delta (G)\) denotes the maximum degree of G. In this work, we offer a provocative question that is: “Is there any polynomial function f such that for every graph G, \(\overrightarrow{\chi _{u}} (G)\le f(\Delta (G))\)?”. Towards this question, we introduce some lower and upper bounds on their parameter of interest. Also, we prove that for every tree T, \(\overrightarrow{\chi _{u}}(T)={\mathcal {O}}(\Delta ^3) \). Next, we show that for a given 3-regular graph G, the universal labeling number of G is 4 if and only if G belongs to Class 1. Therefore, for a given 3-regular graph G, it is an \( {{\mathbf {N}}}{{\mathbf {P}}} \)-complete to determine whether the universal labeling number of G is 4. Finally, using probabilistic methods, we almost confirm a weaker version of the problem.     

Distance domination in graphs with given minimum and maximum degree

For an integer \(k \ge 1\), a distance k-dominating set of a connected graph G is a set S of vertices of G such that every vertex of V(G) is at distance at most k from some vertex of S. The distance k-domination number \(\gamma _k(G)\) of G is the minimum cardinality of a distance k-dominating set of G. In this paper, we establish an upper bound on the distance k-domination number of a graph in terms of its order, minimum degree and maximum degree. We prove that for \(k \ge 2\), if G is a connected graph with minimum degree \(\delta \ge 2\) and maximum degree \(\Delta \) and of order \(n \ge \Delta + k - 1\), then \(\gamma _k(G) \le \frac{n + \delta - \Delta }{\delta + k - 1}\). This result improves existing known results.     

Total edge irregularity strength of accordion graphs

An edge irregular total k-labeling \(\varphi : V\cup E \rightarrow \{ 1,2, \dots , k \}\) of a graph \(G=(V,E)\) is a labeling of vertices and edges of G in such a way that for any different edges xy and \(x'y'\) their weights \(\varphi (x)+ \varphi (xy) + \varphi (y)\) and \(\varphi (x')+ \varphi (x'y') + \varphi (y')\) are distinct. The total edge irregularity strength, tes(G), is defined as the minimum k for which G has an edge irregular total k-labeling. We have determined the exact value of the total edge irregularity strength of accordion graphs.     

Improved upper bound for the degenerate and star chromatic numbers of graphs

Let \(G=G(V,E)\) be a graph. A proper coloring of G is a function \(f:V\rightarrow N\) such that \(f(x)\ne f(y)\) for every edge \(xy\in E\). A proper coloring of a graph G such that for every \(k\ge 1\), the union of any k color classes induces a \((k-1)\)-degenerate subgraph is called a degenerate coloring; a proper coloring of a graph with no two-colored \(P_{4}\) is called a star coloring. If a coloring is both degenerate and star, then we call it a degenerate star coloring of graph. The corresponding chromatic number is denoted as \(\chi _{sd}(G)\). In this paper, we employ entropy compression method to obtain a new upper bound \(\chi _{sd}(G)\le \lceil \frac{19}{6}\Delta ^{\frac{3}{2}}+5\Delta \rceil \) for general graph G.