Nonnegative signed total Roman domination in graphs by Nasrin Dehgardi, Lutz Volkmann

“…In addition, if $G$ is a bipartite graph of order $n$, then we prove that $\gamma^{NN}_{stR}(G)\ge \frac{3}{2}(\sqrt{4n+1}-1)-n$.…”

On Factorable Bigraphic Pairs by Yin Jian-Hua, Li Sha-Sha

“…We say that S is a bigraphic pair if there exists a simple bipartite graph G with partite sets {x1, x2, . . . , xm} and {y1, y2, . . . , yn} such that dG(xi) = ai for 1 ≤ i ≤ m and dG(yj) = bj for 1 ≤ j ≤ n. …”
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BTDM: A Bi-Directional Translating Decoding Model-Based Relational Triple Extraction by Zhi Zhang, Junan Yang, Hui Liu, Pengjiang Hu

“…Finally, a (entity pair, relation) bipartite graph is designed to achieve practical relationship judgement. …”
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Diversity, Prevalence And Host Specificity Of Parasites In Freshwater Fish Population In Selected Reservoirs Of Perak River, Perak by Ibrahim, Ado Abdulmalik

“…The host-parasites interactions were then visualized by a bipartite graph, followed up by the analysis of the effects of fish parasites on the relative condition factor (Kn), and the relationship of parasites with the water temperature, pH, and dissolved oxygen (DO) of the reservoirs. …”
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Mapping ontology vertices to a line using hypergraph framework by Linli Zhu, Gang Hua, Wei Gao

“…Each set of compared ontology vertices constitutes a hyperedge, and thus the ontology sample sets and the computational framework are represented by hypergraph and its associated bipartite graph. The algorithm proposed in this paper has potential guiding significance and theoretical value for engineering applications. …”
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DNN-MVL: DNN-Multi-View-Learning-Based Recover Block Missing Data in a Dam Safety Monitoring System by Yingchi Mao, Jianhua Zhang, Hai Qi, Longbao Wang

“…These five views are modeled with inverse distance of weight interpolation, bidirectional simple exponential smoothing, user-based collaborative filtering, mass diffusion-based collaborative filtering with the bipartite graph, and structural embedding, respectively. …”
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Progress on Roman and Weakly Connected Roman Graphs by Joanna Raczek, Rita Zuazua

“…In this paper, we show that the decision problem of whether a bipartite graph is Roman is a co-NP-hard problem. Next, we prove similar results for weakly connected Roman graphs. …”
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Link-State Aware Hybrid Routing in the Terrestrial–Satellite Integrated Network by Huihui Xu, Zhangsong Shi, Mingliu Liu, Ning Zhang, Yanjun Yan, Guangjie Han

“…For the terrestrial–satellite link in hybrid routing, the data transmission problem is transformed into a weighted bipartite graph matching problem and solved with a Kuhn–Munkres-based link selection algorithm. …”
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A Community-Driven Deep Collaborative Approach for Recommender Systems by Sofia Bourhim, Lamia Benhiba, M. A. Janati Idrissi

“…It extracts the overlapping communities from the homophily user-user graph and also integrates the high-order information from the user-item bipartite graph. We conduct experiments and evaluate the DGCF on the MovieLens datasets (ML-100K and ML-1M), and Douban dataset. …”
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Identifying the Author Group of Malwares through Graph Embedding and Human-in-the-Loop Classification by Dong-Kyu Chae, Sung-Jun Park, Eujeanne Kim, Jiwon Hong, Sang-Wook Kim

“…Our framework consists of a malware-feature bipartite graph construction, malware embedding based on DeepWalk, and classification of the target malware based on the k-nearest neighbors (KNN) classification. …”
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Exploring gene-patient association to identify personalized cancer driver genes by linear neighborhood propagation by Yiran Huang, Fuhao Chen, Hongtao Sun, Cheng Zhong

“…LPDriver builds personalized gene network based on the genetic data of individual patients, extracts the gene-patient associations from the bipartite graph of the personalized gene network and utilizes a linear neighborhood propagation model to mine gene-patient associations to detect personalized driver genes. …”
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Economic Pricing in Peer-to-Peer Electrical Trading for a Sustainable Electricity Supply Chain Industry in Thailand by Adisorn Leelasantitham, Thammavich Wongsamerchue, Yod Sukamongkol

“…Then, information was obtained to analyze the trading price trends by using the law of demand and supply in addition to the principle of the bipartite graph. The price trend results agree well with those of price equilibrium equations. …”
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Join Products <i>K</i>_2,3 + <i>C_n</i> by Michal Staš

“…The main goal of the paper is to state the crossing number of the join product <inline-formula> <math display="inline"> <semantics> <mrow> <msub> <mi>K</mi> <mrow> <mn>2</mn> <mo>,</mo> <mn>3</mn> </mrow> </msub> <mo>+</mo> <msub> <mi>C</mi> <mi>n</mi> </msub> </mrow> </semantics> </math> </inline-formula> for the complete bipartite graph <inline-formula> <math display="inline"> <semantics> <msub> <mi>K</mi> <mrow> <mn>2</mn> <mo>,</mo> <mn>3</mn> </mrow> </msub> </semantics> </math> </inline-formula>, where <inline-formula> <math display="inline"> <semantics> <msub> <mi>C</mi> <mi>n</mi> </msub> </semantics> </math> </inline-formula> is the cycle on <i>n</i> vertices. …”
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Self-Attention Based Sequential Recommendation With Graph Convolutional Networks by Dewen Seng, Jingchang Wang, Xuefeng Zhang

“…GCN integrates the user-item interaction as the bipartite graph structure into the embedding process, which can better represent sparse data, but cannot capture users&#x2019; long-term interests. …”
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Zarankiewicz’s problem for semilinear hypergraphs by Abdul Basit, Artem Chernikov, Sergei Starchenko, Terence Tao, Chieu-Minh Tran

“…A bipartite graph $H = \left (V_1, V_2; E \right )$ with $\lvert V_1\rvert + \lvert V_2\rvert = n$ is semilinear if $V_i \subseteq \mathbb {R}^{d_i}$ for some $d_i$ and the edge relation E consists of the pairs of points $(x_1, x_2) \in V_1 \times V_2$ satisfying a fixed Boolean combination of s linear equalities and inequalities in $d_1 + d_2$ variables for some s. …”
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Antenna Selection Based on Matching Theory for Uplink Cell-Free Millimetre Wave Massive Multiple Input Multiple Output Systems by Abdulrahman Al Ayidh, Yusuf Sambo, Sofiat Olaosebikan, Shuja Ansari, Muhammad Ali Imran

“…Therefore, an assignment optimization problem based on a bipartite graph is formulated for cell-free mm-Wave massive MIMO system uplinks. …”
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Exploring tumor-normal cross-talk with TranNet: Role of the environment in tumor progression. by Bayarbaatar Amgalan, Chi-Ping Day, Teresa M Przytycka

“…TranNet infers a sparse weighted bipartite graph from gene expression profiles of matched control samples to tumors. …”
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Calculating Crossing Numbers of Graphs Using Their Redrawings by Michal Staš

“…The connected graph <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mi>G</mi><mo>*</mo></msup></semantics></math></inline-formula> of order six is isomorphic to <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>K</mi><mrow><mn>3</mn><mo>,</mo><mn>3</mn></mrow></msub><mo>\</mo><mi>e</mi></mrow></semantics></math></inline-formula> obtained by removing one edge from the complete bipartite graph <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>K</mi><mrow><mn>3</mn><mo>,</mo><mn>3</mn></mrow></msub></semantics></math></inline-formula>, and the discrete graph <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>D</mi><mi>n</mi></msub></semantics></math></inline-formula> consists of <i>n</i> isolated vertices. …”
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Crater Detection and Recognition Method for Pose Estimation by Zihao Chen, Jie Jiang

“…In stage 2, taking the encoded features and intersection over union (IOU) of craters as weights, we solve the weighted bipartite graph matching problem, which is matching craters in the image with the previously identified craters and the pre-established craters database. …”
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Deep Disentangled Collaborative Filtering with Graph Global Information by HAO Jingyu, WEN Jingxuan, LIU Huafeng, JING Liping, YU Jian

“…GCN-based collaborative filtering models generate the representation of user nodes and item nodes by aggregating information on user-item interaction bipartite graph,and then predict users' preferences on items.However,they neglect users' different interaction intents and cannot fully explore the relationship between users and items.Existing graph disentangled collaborative filtering models model users' interaction intents,but ignore the global information of interaction graph and the essential features of users and items,causing the incompleteness of representation semantics.Furthermore,disentangled representation learning is inefficient due to the iterative structure of model.To solve these problems,this paper devises a deep disentangled collaborative filtering model incorporating graph global information,which is named as global graph disentangled collaborative filtering(G2DCF).G2DCF builds graph global channel and graph disentangled channel,which learns essential features and intent features,respectively.Meanwhile,by introducing orthogonality constraint and representation independence constraint,G2DCF makes every user-item interaction intent as unique as possible to prevent intent degradation,and raises the independence of representations under different intents,so as to improve the disentanglement effect.Compared with the previous graph collaborative filtering models,G2DCF can more comprehensively describe features of users and items.A number of experiments are conducted on three public datasets,and results show that the proposed method outperforms the comparison methods on multiple metrics.Further,this paper analyzes the representation distributions from independence and uniformity,verifies the disentanglement effect.It also compares the convergence speed to verify the effectiveness.…”
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