An inequality that relates the size of a bipartite graph with its order and restrained domination number

Let \(G=(V,E)\) be a graph. A set \(S\subseteq V\) is a restrained dominating set if every vertex in \(V-S\) is adjacent to a vertex in \(S\) and to a vertex in \(V-S\). The restrained domination number of \(G\), denoted \(\gamma _{r}(G)\), is the smallest cardinality of a restrained dominating set of \(G\). Consider a bipartite graph \(G\) of order \(n\ge 4,\) and let \(k\in \{2,3,...,n-2\}.\) In this paper we will show that if \(\gamma _{r}(G)=k\), then \(m\le ((n-k)(n-k+6)+4k-8)/4\). We will also show that this bound is best possible.     

Roman game domination number of a graph

The Roman game domination number of an undirected graph G is defined by the following game. Players \(\mathcal {A}\) and \(\mathcal {D}\) orient the edges of the graph G alternately, with \(\mathcal {D}\) playing first, until all edges are oriented. Player \(\mathcal {D}\) (frequently called Dominator) tries to minimize the Roman domination number of the resulting digraph, while player \(\mathcal {A}\) (Avoider) tries to maximize it. This game gives a unique number depending only on G, if we suppose that both \(\mathcal {A}\) and \(\mathcal {D}\) play according to their optimal strategies. This number is called the Roman game domination number of G and is denoted by \(\gamma _{Rg}(G)\). In this paper we initiate the study of the Roman game domination number of a graph and we establish some bounds on \(\gamma _{Rg}(G)\). We also determine the Roman game domination number for some classes of graphs.     

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.     

Edge-disjoint spanning trees and the number of maximum state circles of a graph

Motivated by the connection with the genus of unoriented alternating links, Jin et al. (Acta Math Appl Sin Engl Ser, 2015) introduced the number of maximum state circles of a plane graph G, denoted by \(s_{\max }(G)\), and proved that \(s_{\max }(G)=\max \{e(H)+2c(H)-v(H)|\) H is a spanning subgraph of \(G\}\), where e(H), c(H) and v(H) denote the size, the number of connected components and the order of H, respectively. In this paper, we show that for any (not necessarily planar) graph G, \(s_{\max }(G)\) can be achieved by the spanning subgraph H of G whose each connected component is a maximal subgraph of G with two edge-disjoint spanning trees. Such a spanning subgraph is proved to be unique and we present a polynomial-time algorithm to find such a spanning subgraph for any graph G.     

Minimum number of disjoint linear forests covering a planar graph

Graph coloring has interesting real-life applications in optimization, computer science and network design, such as file transferring in a computer network, computation of Hessians matrix and so on. In this paper, we consider one important coloring, linear arboricity, which is an improper edge coloring. Moreover, we study linear arboricity on planar graphs with maximum degree \(\varDelta \ge 7\) . We have proved that the linear arboricity of \(G\) is \(\lceil \frac{\varDelta }{2}\rceil \) , if for each vertex \(v\in V(G)\) , there are two integers \(i_v,j_v\in \{3,4,5,6,7,8\}\) such that any two cycles of length \(i_v\) and \(j_v\) , which contain \(v\) , are not adjacent. Clearly, if \(i_v=i, j_v=j\) for each vertex \(v\in V(G)\) , then we can easily get one corollary: for two fixed integers \(i,j\in \{3,4,5,6,7,8\}\) , if there is no adjacent cycles with length \(i\) and \(j\) in \(G\) , then the linear arboricity of \(G\) is \(\lceil \frac{\varDelta }{2}\rceil \) .     

The total {k}-domatic number of a graph

For a positive integer k, a total {k}-dominating function of a graph G is a function f from the vertex set V(G) to the set {0,1,2,…,k} such that for any vertex v∈V(G), the condition ∑ _u∈N(v) f(u)≥k is fulfilled, where N(v) is the open neighborhood of v. A set {f ₁,f ₂,…,f _d } of total {k}-dominating functions on G with the property that ?_i=1^df_i(v) ￡ ksum_{i=1}^{d}f_{i}(v)le k for each v∈V(G), is called a total {k}-dominating family (of functions) on G. The maximum number of functions in a total {k}-dominating family on G is the total {k}-domatic number of G, denoted by d_t^{k}(G)d_{t}^{{k}}(G). Note that d_t^{1}(G)d_{t}^{{1}}(G) is the classic total domatic number d _t (G). In this paper we initiate the study of the total {k}-domatic number in graphs and we present some bounds for d_t^{k}(G)d_{t}^{{k}}(G). Many of the known bounds of d _t (G) are immediate consequences of our results.     

Equality in a bound that relates the size and the restrained domination number of a graph

Let \(G=(V,E)\) be a graph. A set \(S\subseteq V\) is a restrained dominating set if every vertex in \(V-S\) is adjacent to a vertex in \(S\) and to a vertex in \(V-S\). The restrained domination number of \(G\), denoted \(\gamma _{r}(G)\), is the smallest cardinality of a restrained dominating set of \(G\). The best possible upper bound \(q(n,k)\) is established in Joubert (Discrete Appl Math 161:829–837, 2013) on the size \(m(G)\) of a graph \(G\) with a given order \(n \ge 5\) and restrained domination number \(k \in \{3, \ldots , n-2\}\). We extend this result to include the cases \(k=1,2,n\), and characterize graphs \(G\) of order \(n \ge 1\) and restrained domination number \(k \in \{1,\dots , n-2,n\}\) for which \(m(G)=q(n,k)\).     

Faster algorithm to find anti-risk path between two nodes of an undirected graph

For a weighted 2-edge connected graph G=(V,E), we are to find a “minimum risk path” from source s to destination t. This is a shortest s?t path under the assumption that at most one edge on the path may be blocked. The fact that the edge is blocked is known only when we reach a site adjacent to the blocked edge. If n and m are the number of nodes and edges of G, then we show that this problem can be solved in O(n ²) time using only simple data structures. This is an improvement over the previous O(mn+n ²logn) time algorithm. Moreover, with use of more complicated data structures like Fibonacci Heaps and transmuters the time can be further reduced to O(m+nlogn).     

On the relation between Wiener index and eccentricity of a graph

Journal of Combinatorial Optimization - The relation between the Wiener index W(G) and the eccentricity $$\varepsilon (G)$$ of a graph G is studied. Lower and upper bounds on W(G) in terms of...     

Relationship between boardroom independence and corporate performance: Reflections and perspectives

The perceived economic value of an independent boardroom configuration has progressively emerged as a matter of considerable importance in the academic and popular literature. The normative research paradigm has fundamentally been dominated by positivists who formulate inferential models populated by large sets of archival data. Regrettably, however, several decades of intense inquiries and passionate debates have invariably failed to ascertain (or dispel) the economic value of an independent boardroom configuration. The lingering boardroom independence–corporate performance saga has reached an impasse with no clear resolution in the foreseeable future. In this study, I provide a diagnosis (through the thematic analysis of semi-structured interviews) of why the economic viability of an independent boardroom remains an elusive phenomenon for positivist researchers. A central reason for the research impasse is attributed to ontological complexities intrinsic to the very nature of the corporation, compounded by multiple layers of methodological complexities. Ultimately, the disentanglement of this enigma would require a pivotal reconceptualization of the corporate governance research agenda.     

Is there an optimum number of night shifts? Relationship between sleep, health and well-being

By concentrating on the impact of a specific shift-system feature on the well-being of those concerned, rather than on the impact of the shift system as a whole, one might be able to offer more meaningful suggestions as to what constitutes a better form of shift system. The present study focused on the impact of the number of consecutive night shifts worked on the health and well-being of two groups of nurses (permanent night and rotating shift). All nurses completed a copy of the Standard Shiftwork Index, which is a set of questionnaires designed for comparing the effects of different types of shift system on large groups of workers. It includes measurements of psychological ill-health, physical ill-health, chronic fatigue, social and domestic disruption, attitudes towards shiftwork, sleep quality and sleep habits. Results showed clearly the impact of the number of consecutive nights worked on health and well-being, not directly, but indirectly through the impact on sleep duration and sleep quality. Sleep duration was shown to increase with more consecutive nights worked. This in turn was found to predict sleep quality, which in turn was found to be the stronger direct predictor of psychological and physical ill-health: i.e. better health was associated with longer and better quality sleeps. Explanations in terms of circadian adaptation are discussed.     

从管理与文化的关系看中国式管理

有关管理与文化的争论不应再纠缠于文化是否影响管理,而应该去研究文化究竟如何影响管理实践,以及如何在管理理论中考虑文化要素。文化不仅对管理实践具有重要的影响作用,而且对管理理论来说更是建构地方性管理知识体系的基点。在中国的管理研究中,对文化的不同处理构成了3种研究途径:管理中国化研究、中国管理研究以及管理普适性研究。从当前中国实践的需求来看,中国管理研究是最为迫切需要的。中国式管理不仅存在,而且应成为中国学者研究的重要领域。     

会计信息质量与过度投资的关系研究

以我国2004～2006年制造业上市公司的数据为样本,对会计信息质量和企业过度投资的关系进行了实证研究.结果发现:会计信息质量与企业过度投资存在显著负相关,提高会计信息质量可以抑制企业的过度投资行为;在自由现金流量较多的上市公司中,会计信息质量与过度投资呈现出更强的负相关,提高会计信息质量能对该类企业的过度投资产生更大的治理效应.这为我国治理企业过度投资提供了新的路径.     

A new graph parameter and a construction of larger graph without increasing radio <Emphasis Type="Italic">k</Emphasis>-chromatic number

For a positive integer \(k\ge 2\), the radio k-coloring problem is an assignment L of non-negative integers (colors) to the vertices of a finite simple graph G satisfying the condition \(|L(u)-L(v)| \ge k+1-d(u,v)\), for any two distinct vertices u, v of G and d(u, v) being distance between u, v. The span of L is the largest integer assigned by L, while 0 is taken as the smallest color. An \(rc_k\)-coloring on G is a radio k-coloring on G of minimum span which is referred as the radio k-chromatic number of G and denoted by \(rc_k(G)\). An integer h, \(0<h<rc_k(G)\), is a hole in a \(rc_k\)-coloring on G if h is not assigned by it. In this paper, we construct a larger graph from a graph of a certain class by using a combinatorial property associated with \((k-1)\) consecutive holes in any \(rc_k\)-coloring of a graph. Exploiting the same property, we introduce a new graph parameter, referred as \((k-1)\)-hole index of G and denoted by \(\rho _k(G)\). We also explore several properties of \(\rho _k(G)\) including its upper bound and relation with the path covering number of the complement \(G^c\).     

盈余惯性与价格惯性的关系研究

Fama认为,盈余惯性与价格惯性是仅有的两个对有效市场假说形成真正威胁的、持续的、稳健的市场异象。本文参考Chan等、Chordia和Shivakumar的研究方法,考察我国股市盈余惯性与价格惯性的关系。研究部分支持了Chordia和Shivakumar所提出的噪声代理变量假说,而未支持Chan等所提出的多种信息源假说。我国股市特殊的信息披露环境与投资者行为特征可以解释本文的研究结论。     

网络使用程度对企业销售效率影响的实证研究

本文利用对近百家企业问卷调查获得的数据,运用线性回归和非参数检验等方法,证明了我国企业的网络使用程度与其销售效率之间的关系,并进一步分析了不同网络工具对销售效率提高的差异化影响,最后对企业未来的网络应用提出了一些切实的建议。     

Auditor independence, corporate governance and aggressive financial reporting: an empirical analysis

This paper seeks to provide empirical evidence on the efficacy of three important governance mechanisms (auditors, directors, and institutional shareholders) in constraining aggressive financial reporting, proxied by abnormal accruals. It also examines the effects of the Sarbanes–Oxley Act (SOX) on their efficacy. Using a sample of US firms audited by the Big 5 (4) auditors between 2000 and 2004, we document a positive relation between abnormal accruals (our proxy for financial reporting aggressiveness) and auditors’ economic dependence on their clients. Furthermore, we find that this relation is driven by firms with weak non-auditor governance mechanisms before and after the enactment of SOX. The results suggest that aggressive financial reporting occurs only when multiple governance mechanisms ‘fail’. More specifically, such type of reporting requires that a highly dependent auditor operates in a ‘poor’ governance setting. Thus, the paper underscores the importance of strong governance in constraining aggressive financial reporting. Moreover, our results suggest that governance regulation (such as SOX) is not a substitute for strong governance mechanisms and thus caution against the over reliance on SOX-type legislation in other parts of the world.