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Journal articles on the topic 'Intersection digraphs'

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Author: Grafiati

Published: 18 May 2024

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1

Cary, Michael. "Vertices with the second neighborhood property in Eulerian digraphs." Opuscula Mathematica 39, no. 6 (2019): 765–72. http://dx.doi.org/10.7494/opmath.2019.39.6.765.

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The Second Neighborhood Conjecture states that every simple digraph has a vertex whose second out-neighborhood is at least as large as its first out-neighborhood, i.e. a vertex with the Second Neighborhood Property. A cycle intersection graph of an even graph is a new graph whose vertices are the cycles in a cycle decomposition of the original graph and whose edges represent vertex intersections of the cycles. By using a digraph variant of this concept, we prove that Eulerian digraphs which admit a simple cycle intersection graph not only adhere to the Second Neighborhood Conjecture, but that local simplicity can, in some cases, also imply the existence of a Seymour vertex in the original digraph.

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2

Chiaselotti, G., and T. Gentile. "Intersection properties of maximal directed cuts in digraphs." Discrete Mathematics 340, no. 1 (January 2017): 3171–75. http://dx.doi.org/10.1016/j.disc.2016.07.003.

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3

Liu, Xujun, Roberto Assis Machado, and Olgica Milenkovic. "Directed Intersection Representations and the Information Content of Digraphs." IEEE Transactions on Information Theory 67, no. 1 (January 2021): 347–57. http://dx.doi.org/10.1109/tit.2020.3033168.

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4

Lin, In-Jen, Malay K. Sen, and Douglas B. West. "Intersection representation of digraphs in trees with few leaves." Journal of Graph Theory 32, no. 4 (December 1999): 340–53. http://dx.doi.org/10.1002/(sici)1097-0118(199912)32:4<340::aid-jgt3>3.0.co;2-r.

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5

Akram, Muhammad, Wieslaw A. Dudek, and M. Murtaza Yousaf. "Regularity in Vague Intersection Graphs and Vague Line Graphs." Abstract and Applied Analysis 2014 (2014): 1–10. http://dx.doi.org/10.1155/2014/525389.

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Fuzzy graph theory is commonly used in computer science applications, particularly in database theory, data mining, neural networks, expert systems, cluster analysis, control theory, and image capturing. A vague graph is a generalized structure of a fuzzy graph that gives more precision, flexibility, and compatibility to a system when compared with systems that are designed using fuzzy graphs. In this paper, we introduce the notion of vague line graphs, and certain types of vague line graphs and present some of their properties. We also discuss an example application of vague digraphs.

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6

Jr, Walter D. Morris,. "Acyclic digraphs giving rise to complete intersections." Journal of Commutative Algebra 11, no. 2 (April 2019): 241–64. http://dx.doi.org/10.1216/jca-2019-11-2-241.

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7

MCCLURE, MARK. "INTERSECTIONS OF SELF-SIMILAR SETS." Fractals 16, no. 02 (June 2008): 187–97. http://dx.doi.org/10.1142/s0218348x08003909.

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8

Szegő, László. "On covering intersecting set-systems by digraphs." Discrete Mathematics 234, no. 1-3 (May 2001): 187–89. http://dx.doi.org/10.1016/s0012-365x(00)00381-2.

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9

Jonsson, Jakob. "On the number of Euler trails in directed graphs." MATHEMATICA SCANDINAVICA 90, no. 2 (June 1, 2002): 191. http://dx.doi.org/10.7146/math.scand.a-14370.

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Let $G$ be an Eulerian digraph with all in- and out-degrees equal to 2, and let $\pi$ be an Euler trail in $G$. We consider an intersection matrix $\boldsymbol {L}(\pi)$ with the property that the determinant of $\boldsymbol{L}(\pi) + \boldsymbol{I}$ is equal to the number of Euler trails in $G$; $\boldsymbol{I}$ denotes the identity matrix. We show that if the inverse of $\boldsymbol{L}(\pi)$ exists, then $\boldsymbol{L}^{-1}(\pi) = \boldsymbol{L}(\sigma)$ for a certain Euler trail $\sigma$ in $G$. Furthermore, we use properties of the intersection matrix to prove some results about how to divide the set of Euler trails in a digraph into smaller sets of the same size.

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10

Kurauskas, Valentas. "On small subgraphs in a random intersection digraph." Discrete Mathematics 313, no. 7 (April 2013): 872–85. http://dx.doi.org/10.1016/j.disc.2012.12.024.

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11

Bloznelis, Mindaugas. "A random intersection digraph: Indegree and outdegree distributions." Discrete Mathematics 310, no. 19 (October 2010): 2560–66. http://dx.doi.org/10.1016/j.disc.2010.06.018.

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12

Por, Lip Yee, Chin Soon Ku, and Tan Fong Ang. "Preventing Shoulder-Surfing Attacks using Digraph Substitution Rules and Pass-Image Output Feedback." Symmetry 11, no. 9 (August 30, 2019): 1087. http://dx.doi.org/10.3390/sym11091087.

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In this paper, we focus on methods to prevent shoulder-surfing attacks. We initially adopted digraph substitution rules from PlayFair cipher as our proposed method. PlayFair cipher is a modern cryptography method, which exists at the intersection of the disciplines of mathematics and computer science. However, according to our preliminary study it was insufficient to prevent shoulder-surfing attacks. Thus, a new method had to be proposed. In this new proposed method, we improvised the digraph substitution rules and used these rules together with an output feedback method to determine a pass-image. Our proposed method was evaluated with a user study. The results showed our proposed method was robust against both direct observation and video-recorded shoulder-surfing attacks.

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13

Strnad, William. "ON SHADOW AND FORM: KOREAN NATIONALISM’S DIGRAPHIC CONFLICT." International Journal of Korean Humanities and Social Sciences 2 (November 1, 2016): 87–122. http://dx.doi.org/10.14746/kr.2016.02.06.

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This paper is an examination of the many points of intersection between Korean nationalism in both Koreas, and Chinese characters (Hanja), as well as a contextualization of the historical and, at times, antithetical relationship or binary consisting of Hanja and Han’gŭl (Chosŏn’gŭl). Emerging from liberation the two Korean states over the next several decades would “engage” Hanja with diverse and fluctuating positions and approaches at different times. These responses have ranged from the abolition of Hanja or the enforcement of Han’gŭl (Chosŏn’gŭl) exclusivity, to the re-establishment and strengthening of Hanja education. Koreans for over a century have responded to “issues of script” based on socially-created narratives. This phenomenon can be viewed through constructivist paradigms, or can be interpreted as implemented pragmatic policies exemplifying instrumentalist nationalism. This paper’s assertion is that Korea’s vacillating response regarding Korean nationalism’s digraphic conflict is eloquent of the complex confluences that formed Korean ethnic nationalism, and therefore, Korean national identity.

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14

Jaffke, Lars, O‐joung Kwon, and Jan Arne Telle. "Classes of intersection digraphs with good algorithmic properties." Journal of Graph Theory, December 18, 2023. http://dx.doi.org/10.1002/jgt.23065.

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AbstractWhile intersection graphs play a central role in the algorithmic analysis of hard problems on undirected graphs, the role of intersection digraphs in algorithms is much less understood. We present several contributions towards a better understanding of the algorithmic treatment of intersection digraphs. First, we introduce natural classes of intersection digraphs that generalize several classes studied in the literature. Second, we define the directed locally checkable vertex (DLCV) problems, which capture many well‐studied problems on digraphs, such as (Independent) Dominating Set, Kernel, and ‐Homomorphism. Third, we give a new width measure of digraphs, bi‐mim‐width, and show that the DLCV problems are polynomial‐time solvable when we are provided a decomposition of small bi‐mim‐width. Fourth, we show that several classes of intersection digraphs have bounded bi‐mim‐width, implying that we can solve all DLCV problems on these classes in polynomial time given an intersection representation of the input digraph. We identify reflexivity as a useful condition to obtain intersection digraph classes of bounded bi‐mim‐width, and therefore to obtain positive algorithmic results.

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15

Bergougnoux, Benjamin, Eduard Eiben, Robert Ganian, Sebastian Ordyniak, and M. S. Ramanujan. "Towards a Polynomial Kernel for Directed Feedback Vertex Set." Algorithmica, November 4, 2020. http://dx.doi.org/10.1007/s00453-020-00777-5.

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Abstract In the Directed Feedback Vertex Set (DFVS) problem, the input is a directed graph D and an integer k. The objective is to determine whether there exists a set of at most k vertices intersecting every directed cycle of D. DFVS was shown to be fixed-parameter tractable when parameterized by solution size by Chen et al. (J ACM 55(5):177–186, 2008); since then, the existence of a polynomial kernel for this problem has become one of the largest open problems in the area of parameterized algorithmics. Since this problem has remained open in spite of the best efforts of a number of prominent researchers and pioneers in the field, a natural step forward is to study the kernelization complexity of DFVS parameterized by a natural larger parameter. In this paper, we study DFVS parameterized by the feedback vertex set number of the underlying undirected graph. We provide two main contributions: a polynomial kernel for this problem on general instances, and a linear kernel for the case where the input digraph is embeddable on a surface of bounded genus.

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16

Peixoto, Ana Rita, Ana de Almeida, Nuno António, Fernando Batista, Ricardo Ribeiro, and Elsa Cardoso. "Unlocking the power of Twitter communities for startups." Applied Network Science 8, no. 1 (September 20, 2023). http://dx.doi.org/10.1007/s41109-023-00593-0.

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AbstractSocial media platforms offer cost-effective digital marketing opportunities to monitor the market, create user communities, and spread positive opinions. They allow companies with fewer budgets, like startups, to achieve their goals and grow. In fact, studies found that startups with active engagement on those platforms have a higher chance of succeeding and receiving funding from venture capitalists. Our study explores how startups utilize social media platforms to foster social communities. We also aim to characterize the individuals within these communities. The findings from this study underscore the importance of social media for startups. We used network analysis and visualization techniques to investigate the communities of Portuguese IT startups through their Twitter data. For that, a social digraph has been created, and its visualization shows that each startup created a community with a degree of intersecting followers and following users. We characterized those users using user node-level measures. The results indicate that users who are followed by or follow Portuguese IT startups are of these types: “Person”, “Company,” “Blog,” “Venture Capital/Investor,” “IT Event,” “Incubators/Accelerators,” “Startup,” and “University.” Furthermore, startups follow users who post high volumes of tweets and have high popularity levels, while those who follow them have low activity and are unpopular. The attained results reveal the power of Twitter communities and offer essential insights for startups to consider when building their social media strategies. Lastly, this study proposes a methodological process for social media community analysis on platforms like Twitter.

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