Total and forcing total edge-to-vertex monophonic number of a graph

For a connected graph \(G = \left( V,E\right) \), a set \(S\subseteq E(G)\) is called a total edge-to-vertex monophonic set of a connected graph G if the subgraph induced by S has no isolated edges. The total edge-to-vertex monophonic number \(m_{tev}(G)\) of G is the minimum cardinality of its total edge-to-vertex monophonic set of G. The total edge-to-vertex monophonic number of certain classes of graphs is determined and some of its general properties are studied. Connected graphs of size \(q \ge 3 \) with total edge-to-vertex monophonic number q is characterized. It is shown that for positive integers \(r_{m},d_{m}\) and \(l\ge 4\) with \(r_{m}< d_{m} \le 2 r_{m}\), there exists a connected graph G with \(\textit{rad}_ {m} G = r_{m}\), \(\textit{diam}_ {m} G = d_{m}\) and \(m_{tev}(G) = l\) and also shown that for every integers a and b with \(2 \le a \le b\), there exists a connected graph G such that \( m_{ev}\left( G\right) = b\) and \(m_{tev}(G) = a + b\). A forcing subset for S of minimum cardinality is a minimum forcing subset of S. The forcing total edge-to-vertex monophonic number of S, denoted by \(f_{tev}(S)\) is the cardinality of a minimum forcing subset of S. The forcing total edge-to-vertex monophonic number of G, denoted by \(f_{tev}(G) = \textit{min}\{f_{tev}(S)\}\), where the minimum is taken over all total edge-to-vertex monophonic set S in G. The forcing total edge-to-vertex monophonic number of certain classes of graphs are determined and some of its general properties are studied. It is shown that for every integers a and b with \(0 \le a \le b\) and \(b \ge 2\), there exists a connected graph G such that \(f_{tev}(G) = a\) and \( m _{tev}(G) = b\), where \( f _{tev}(G)\) is the forcing total edge-to-vertex monophonic number of G.     

The matching extension problem in general graphs is co-NP-complete

A simple connected graph G with 2n vertices is said to be k-extendable for an integer k with \(0<k<n\) if G contains a perfect matching and every matching of cardinality k in G is a subset of some perfect matching. Lakhal and Litzler (Inf Process Lett 65(1):11–16, 1998) discovered a polynomial algorithm that decides whether a bipartite graph is k-extendable. For general graphs, however, it has been an open problem whether there exists a polynomial algorithm. The new result presented in this paper is that the extendability problem is co-NP-complete.     

Reliability evaluation of a multicast over coded packet networks

Network coding is a generalization of conventional routing methods that allows a network node to code information flows before forwarding them. While it has been theoretically proved that network coding can achieve maximum network throughput, theoretical results usually do not consider the stochastic nature in information processing and transmission, especially when the capacity of each arc becomes stochastic due to failure, attacks, or maintenance. Hence, the reliability measurement of network coding becomes an important issue to evaluate the performance of the network under various system settings. In this paper, we present analytical expressions to measure the reliability of multicast communications in coded networks, where network coding is most promising. We define the probability that a multicast rate can be transmitted through a coded packet network under a total transmission cost constraint as the reliability metric. To do this, we first introduce an exact mathematical formulation to construct multicast connections over coded packet networks under a limited transmission cost. We then propose an algorithm based on minimal paths to calculate the reliability measurement of multicast connections and analyze the complexity of the algorithm. Our results show that the reliability of multicast routing with network coding improved significantly compared to the case of multicast routing without network coding.     

On the <Emphasis Type="Italic">m</Emphasis>-clique free interval subgraphs polytope: polyhedral analysis and applications

In this paper we study the m-clique free interval subgraphs. We investigate the facial structure of the polytope defined as the convex hull of the incidence vectors associated with these subgraphs. We also present some facet-defining inequalities to strengthen the associated linear relaxation. As an application, the generalized open-shop problem with disjunctive constraints (GOSDC) is considered. Indeed, by a projection on a set of variables, the m-clique free interval subgraphs represent the solution of an integer linear program solving the GOSDC presented in this paper. Moreover, we propose exact and heuristic separation algorithms, which are exploited into a Branch-and-cut algorithm for solving the GOSDC. Finally, we present and discuss some computational results.     

New lower bounds for the second variable Zagreb index

The aim of this paper is to obtain new sharp inequalities for a large family of topological indices, including the second variable Zagreb index \(M_2^{\alpha }\), and to characterize the set of extremal graphs with respect to them. Our main results provide lower bounds on this family of topological indices involving just the minimum and the maximum degree of the graph. These inequalities are new even for the Randi?, the second Zagreb and the modified Zagreb indices.     

Coopetition in coworking-spaces: value creation and appropriation tensions in an entrepreneurial space

Coopetition has the potential to improve entrepreneurship and innovation. It will be prevalent in coworking-spaces building a growing field for individual and corporate entrepreneurship. The individuals’ physical closeness in the professional and social space of the coworking-space eases multifaceted transfers of explicit and implicit knowledge, stimulating creation, transfer, overhaul, and implementation of entrepreneurial ideas. While entrepreneurs in these coworking-spaces collaborate on sharing knowledge and resources and on finding creative ideas from which can breed new venture concepts, they simultaneously compete on the appropriation of values. Thus, entrepreneurs in coworking-spaces face coopetitive tensions of creating and appropriating the values. Based  on  interview data and secondary sources, this paper explains four different prototype institutions of coworking-spaces: the corporate coworking-space, the open corporate coworking-space, the consultancy coworking-space, and the independent coworking-space. Study explains different tensions of value creation and appropriation that occur within the coopetition in the different forms of coworking-spaces.     

Modelling period fertility: Schooling and intervals following a birth in Eastern Africa

We describe a regression-based approach to the modelling of age-, order-, and duration-specific period fertility, using retrospective survey data. The approach produces results that are free of selection biases and can be used to study differential fertility. It is applied to Demographic and Health Survey data for Ethiopia, Kenya, Tanzania, and Zimbabwe to investigate differential trends in fertility by education. Parity progression fell and the intervals following each birth lengthened between the 1970s and 2000s in all four countries. Fertility fell most among women with secondary education. In contrast to other world regions, postponement of successive births for extended periods accounted for much of the initial drop in fertility in these African countries. However, family size limitation by women with secondary education in Ethiopia and Kenya and longer birth spacing in Zimbabwe also played significant roles. Thus, birth control is being adopted in Eastern Africa in response to diverse changes in fertility preferences.     

Cohort Differences in Parental Financial Help to Adult Children

In this article, we examine birth cohort differences in parents’ provision of monetary help to adult children with particular focus on the extent to which cohort differences in family structure and the transition to adulthood influence these changes. Using data from the Health and Retirement Study from 1994 to 2010, we compare financial help to children of three respondent cohorts as the parents in these birth cohorts from ages 53–58 to 57–62. We find that transfers to children have increased among more recent cohorts. Two trends—declining family size and children’s delay in marriage—account for part of the increase across cohorts. However, other trends, such as the increase in the number of stepchildren and increasing child’s income level, tend to decrease the observed cohort trend.     

Automating argument construction

Over the past five years the Artificial Intelligence Center at SRI has been developing a new technology to address the problem of automated information management within real- world contexts. The result of this work is a body of techniques for automated reasoning from evidence that we call evidential reasoning. The techniques are based upon the mathematics of belief functions developed by Dempster and Shafer and have been successfully applied to a variety of problems including computer vision, multisensor integration, and intelligence analysis.

We have developed both a formal basis and a framework for implementating automated reasoning systems based upon these techniques. Both the formal and practical approach can be divided into four parts: (1) specifying a set of distinct propositional spaces, (2) specifying the interrelationships among these spaces, (3) representing bodies of evidence as belief distributions, and (4) establishing paths of the bodies for evidence to move through these spaces by means of evidential operations, eventually converging on spaces where the target questions can be answered. These steps specify a means for arguing from multiple bodies of evidence toward a particular (probabilistic) conclusion. Argument construction is the process by which such evidential analyses are constructed and is the analogue of constructing proof trees in a logical context.

This technology features the ability to reason from uncertain, incomplete, and occasionally inaccurate information based upon seven evidential operations: fusion, discounting, translation, projection, summarization, interpretation, and gisting. These operation are theoretically sound but have intuitive appeal as well.

In implementing this formal approach, we have found that evidential arguments can be represented as graphs. To support the construction, modification, and interrogation of evidential arguments, we have developed Gister. Gister provides an interactive, menu-driven, graphical interface that allows these graphical structures to be easily manipulated.

Our goal is to provide effective automated aids to domain experts for argument construction. Gister represents our first attempt at such an aid.