Degree Associated Edge Reconstruction Number of Graphs with Regular Pruned Graph

An ecard of a graph $G$ is a subgraph formed by deleting an edge. A da-ecard specifies the degree of the deleted edge along with the ecard. The degree associated edge reconstruction number of a graph $G,~dern(G),$ is the minimum number of da-ecards that uniquely determines $G.$ The adversary degree associated edge reconstruction number of a graph $G, adern(G),$ is the minimum number $k$ such that every collection of $k$ da-ecards of $G$ uniquely determines $G.$ The maximal subgraph without end vertices of a graph $G$ which is not a tree is the pruned graph of $G.$ It is shown that $dern$ of complete multipartite graphs and some connected graphs with regular pruned graph is $1$ or $2.$ We also determine $dern$ and $adern$ of corona product of standard graphs

On some problems in reconstruction

A graph is {\it reconstructible} if it is determined by its {\it deck} of unlabeled subgraphs obtained by deleting one vertex; a {\it card} is one of these subgraphs. The {\it Reconstruction Conjecture} asserts that all graphs with at least three vertices are reconstructible. In Chapter $2$ we consider $k$-deck reconstruction of graphs. The {\it $k$-deck} of a graph is its multiset of $k$-vertex induced subgraphs. We prove a generalization of a result by Bollob\'as concerning the $k$-deck reconstruction of almost all graphs, showing that when $\ell \le (1-\epsilon)\frac{n}{2}$, the probability than an $n$-vertex graph is reconstructible from some $\binom{\ell+1}{2}$ of the graphs in the $(n-\ell)$-deck tends to $1$ as $n$ tends to $\infty$. We determine the smallest $k$ such that all graphs with maximum degree $2$ are $k$-deck reconstructible. We prove for $n\ge 26$ that whether a graph is connected is determined by its $(n-3)$-deck. We prove that if $G$ is a complete $r$-partite graphs, then $G$ is $(r+1)$-deck reconstructible (the same holds for $\overline{G}$). In Chapter $3$ we consider degree-associated reconstruction. An $(n-1)$-vertex induced subgraph accompanied with the degree of the missing vertex is called a {\it dacard}. The {\it degree-associated reconstruction number} of a graph $G$ is the fewest number of dacards needed to determine $G$. We provide a tool for reconstructing some graphs from two dacards. We prove that certain families of trees and disconnected graphs can be reconstructed from two dacards. We also determine the degree-associated reconstruction number for complete multipartite graphs and their complements. For such graphs, we also determine the least $s$ such that {\it every} set of $s$ dacards determine the graph. In Chapter $4$ we consider the reconstruction of matrices from principal submatrices. A $(n-\ell)$-by-$(n-\ell)$ principal submatrix is a submatrix formed by deleting $\ell$ rows and columns symmetrically. The {\it matrix reconstruction threshold} $mrt(\ell)$ is the minimum integer $n_0$ such that for $n\ge n_0$ all $n$-by-$n$ matrices are reconstructible from their deck of $(n-\ell)$-by-$(n-\ell)$ principal submatrices. We prove $mrt(\ell) \leq \frac{2}{\ln 2}\ell^2+3\ell$

HU Record, Vol 15, No. 2

Contents: I. Editorials II. Appreciation of Music - Roy W. Tibbs III. Democracy at Work - Frank H. Wimberly IV. Shylock the Jew - Leonard Z. Johnson V. Financial Report VI. Howard Alumni You Ought to Know VII. Alumni Notes VIII. University Notes IX. Undergraduate Life X. Counterweight

“Fifty Years of Our Whole Voice”: An Examination of the History and Culture Leading to the Publication of Fire!! Devoted to Younger Artists and Aiiieeeee!: An Anthology of Asian American Writers

According to African American literary theorist Henry Louis Gates, “the slave wrote not primarily to demonstrate humane letters, but to demonstrate his or her own membership in the human community” (128). Two efforts at this demonstration of community membership exist in the publication of the literary journal, Fire!!, written and published by African American artists and writers in 1926 and in the anthology AIIIEEEEE!, compiled and edited by Asian American writers and published in 1974. These compilations, published not quite fifty years apart, are direct responses and reactions to the efforts of the larger society to influence and/or to silence the voices of African American and Asian American people in the United States. The Harlem Renaissance artists seem to have spoken to the AIIIEEEEE! editors, who appear to have continued the conversation in their work while demonstrating the importance of historic memory, cultural influence, and national identity. As Fire!! and AIIIEEEEE! talk to each other, they symbolize the double voice that accompanies the dual consciousness of people of color in America and signify a collective effort to redefine the expectations that white America has of people of color. For each of them, the years and events leading to their publications shape the content, the immediate reception, and the longstanding impact of the publications themselves. Together, the works represent the power of multiethnic presence in American literature, and now, years later, texts continue to speak across generations and cultures and in voices strident enough to empower artists and writers and to influence the direction of American literature. Studying literature and art, not in isolation but in relation to other works, even those from other cultures, enhances the significance of collective contribution and appreciation of the literature that expresses national identity and the American place in the global community. To that end, understanding the significance of the cultural and historical contexts that lead to artistic and literary production provides a comprehensive appreciation of Fire!! and AIIIEEEEE! and their creators by revealing connections, tensions, and diversions for analysis, as well as a more complete understanding of the works themselves

An historical review of the role Black parents and the Black community played in providing schooling for Black children in the South, 1865-1954.

The specific purposes of this study were to identify and highlight the many and varied contributions Black people made in providing schooling for their children in the South from 1865 to 1954, and thereby, make a significant contribution to the literature on this subject. This study added weight to the historical importance Blacks have placed on the education of their children. Ignorance of this history affects how Black children are viewed, treated, taught, encouraged, or discouraged in the process of acquiring an education in this society. Fifty-one autobiographies were used as the primary data source. They spanned three major periods--Reconstruction, Post-Reconstruction and the period after World War I to the Brown decision. They were selected on the following criteria: the life of individuals who lived in the Southern region of the United States; and, individuals whose own personal experiences related to formal schooling as students, parents, teachers or community activists. This research, historical and largely descriptive, was designed to investigate the role Black parents and the Black community played in providing schooling for Black children in the South, from 1865 to 1954. These authors, in their own words, reported that their parents and communities placed high value on education and made many sacrifices in order to have their children acquire an education. It is clear from this study that the white authorities in control of the education of all children in America were primarily interested in the education of white children and this fact adversely affected the education of Black children. The research demonstrated that across the periods studied Black children did not have the same educational advantages that white school children had. Further, this study suggests the need to re-examine the issues related to why Black children are not given an equal educational opportunity. To monitor this process, Black parents, as the first teachers, must become more involved in the education of Black children. However, in order to do that the schools must bring Black parents into the system

Albuquerque Evening Citizen, 11-20-1905

https://digitalrepository.unm.edu/abq_citizen_news/3414/thumbnail.jp

Portland Daily Press: September 30,1867

https://digitalmaine.com/pdp_1867/1333/thumbnail.jp