Relevant bibliographies by topics / Non-isomorphic graph

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  1. Journal articles
  2. Dissertations / Theses
  3. Book chapters
  4. Conference papers

Academic literature on the topic 'Non-isomorphic graph'

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Published: 4 June 2021
Last updated: 4 February 2022

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Journal articles on the topic "Non-isomorphic graph"

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Abdollahi, Alireza, Shahrooz Janbaz, and Mojtaba Jazaeri. "Groups all of whose undirected Cayley graphs are determined by their spectra." Journal of Algebra and Its Applications 15, no. 09 (August 22, 2016): 1650175. http://dx.doi.org/10.1142/s0219498816501759.

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The adjacency spectrum [Formula: see text] of a graph [Formula: see text] is the multiset of eigenvalues of its adjacency matrix. Two graphs with the same spectrum are called cospectral. A graph [Formula: see text] is “determined by its spectrum” (DS for short) if every graph cospectral to it is in fact isomorphic to it. A group is DS if all of its Cayley graphs are DS. A group [Formula: see text] is Cay-DS if every two cospectral Cayley graphs of [Formula: see text] are isomorphic. In this paper, we study finite DS groups and finite Cay-DS groups. In particular we prove that a finite DS group is solvable, and every non-cyclic Sylow subgroup of a finite DS group is of order [Formula: see text], [Formula: see text], [Formula: see text] or [Formula: see text]. We also give several infinite families of non-Cay-DS solvable groups. In particular we prove that there exist two cospectral non-isomorphic [Formula: see text]-regular Cayley graphs on the dihedral group of order [Formula: see text] for any prime [Formula: see text].
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Lo Faro, Giovanni, Salvatore Milici, and Antoinette Tripodi. "Uniformly Resolvable Decompositions of Kv-I into n-Cycles and n-Stars, for Even n." Mathematics 8, no. 10 (October 13, 2020): 1755. http://dx.doi.org/10.3390/math8101755.

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If X is a connected graph, then an X-factor of a larger graph is a spanning subgraph in which all of its components are isomorphic to X. Given a set Γ of pairwise non-isomorphic graphs, a uniformly resolvable Γ-decomposition of a graph G is an edge decomposition of G into X-factors for some graph X∈Γ. In this article we completely solve the existence problem for decompositions of Kv-I into Cn-factors and K1,n-factors in the case when n is even.
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SRIDHARAN, N., S. AMUTHA, and S. B. RAO. "INDUCED SUBGRAPHS OF GAMMA GRAPHS." Discrete Mathematics, Algorithms and Applications 05, no. 03 (September 2013): 1350012. http://dx.doi.org/10.1142/s1793830913500122.

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Let G be a graph. The gamma graph of G denoted by γ ⋅ G is the graph with vertex set V(γ ⋅ G) as the set of all γ-sets of G and two vertices D and S of γ ⋅ G are adjacent if and only if |D ∩ S| = γ(G) – 1. A graph H is said to be a γ-graph if there exists a graph G such that γ ⋅ G is isomorphic to H. In this paper, we show that every induced subgraph of a γ-graph is also a γ-graph. Furthermore, if we prove that H is a γ-graph, then there exists a sequence {Gn} of non-isomorphic graphs such that H = γ ⋅ Gn for every n.
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Huang, Shaobin, Jiang Zhou, and Changjiang Bu. "Signless Laplacian spectral characterization of graphs with isolated vertices." Filomat 30, no. 14 (2016): 3689–96. http://dx.doi.org/10.2298/fil1614689h.

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A graph is said to be DQS if there is no other non-isomorphic graph with the same signless Laplacian spectrum. For a DQS graph G, we show that G ? rK1 is DQS under certain conditions. Applying these results, some DQS graphs with isolated vertices are obtained.
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Jain, Vivek, and Pradeep Kumar. "A note on the power graphs of finite nilpotent groups." Filomat 34, no. 7 (2020): 2451–61. http://dx.doi.org/10.2298/fil2007451j.

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The power graph P(G) of a group G is the graph with vertex set G and two distinct vertices are adjacent if one is a power of the other. Two finite groups are said to be conformal, if they contain the same number of elements of each order. Let Y be a family of all non-isomorphic odd order finite nilpotent groups of class two or p-groups of class less than p. In this paper, we prove that the power graph of each group in Y is isomorphic to the power graph of an abelian group and two groups in Y have isomorphic power graphs if they are conformal. We determine the number of maximal cyclic subgroups of a generalized extraspecial p-group (p odd) by determining the power graph of this group. We also determine the power graph of a p-group of order p4 (p odd).
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Costalonga, João Paulo, Robert J. Kingan, and Sandra R. Kingan. "Constructing Minimally 3-Connected Graphs." Algorithms 14, no. 1 (January 1, 2021): 9. http://dx.doi.org/10.3390/a14010009.

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A 3-connected graph is minimally 3-connected if removal of any edge destroys 3-connectivity. We present an algorithm for constructing minimally 3-connected graphs based on the results in (Dawes, JCTB 40, 159-168, 1986) using two operations: adding an edge between non-adjacent vertices and splitting a vertex. To test sets of vertices and edges for 3-compatibility, which depends on the cycles of the graph, we develop a method for obtaining the cycles of G′ from the cycles of G, where G′ is obtained from G by one of the two operations above. We eliminate isomorphic duplicates using certificates generated by McKay’s isomorphism checker nauty. The algorithm consecutively constructs the non-isomorphic minimally 3-connected graphs with n vertices and m edges from the non-isomorphic minimally 3-connected graphs with n−1 vertices and m−2 edges, n−1 vertices and m−3 edges, and n−2 vertices and m−3 edges.
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Shiau, S. Y., R. Joynt, and S. N. Coppersmith. "Physically-motivated dynamical algorithms for the graph isomorphism problem." Quantum Information and Computation 5, no. 6 (September 2005): 492–506. http://dx.doi.org/10.26421/qic5.6-7.

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The graph isomorphism problem (GI) plays a central role in the theory of computational complexity and has importance in physics and chemistry as well \cite{kobler93,fortin96}. No polynomial-time algorithm for solving GI is known. We investigate classical and quantum physics-based polynomial-time algorithms for solving the graph isomorphism problem in which the graph structure is reflected in the behavior of a dynamical system. We show that a classical dynamical algorithm proposed by Gudkov and Nussinov \cite{gudkov02} as well as its simplest quantum generalization fail to distinguish pairs of non-isomorphic strongly regular graphs. However, by combining the algorithm of Gudkov and Nussinov with a construction proposed by Rudolph \cite{rudolph02} in which one examines a graph describing the dynamics of two particles on the original graph, we find an algorithm that successfully distinguishes all pairs of non-isomorphic strongly regular graphs that we tested with up to 29 vertices.
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Zhao, Jinxing, and Guixin Deng. "Remark on subgroup intersection graph of finite abelian groups." Open Mathematics 18, no. 1 (September 18, 2020): 1025–29. http://dx.doi.org/10.1515/math-2020-0066.

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Abstract Let G be a finite group. The subgroup intersection graph \text{Γ}(G) of G is a graph whose vertices are non-identity elements of G and two distinct vertices x and y are adjacent if and only if |\langle x\rangle \cap \langle y\rangle |\gt 1 , where \langle x\rangle is the cyclic subgroup of G generated by x. In this paper, we show that two finite abelian groups are isomorphic if and only if their subgroup intersection graphs are isomorphic.
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Nath, Rajat Kanti, and Jutirekha Dutta. "Spectrum of commuting graphs of some classes of finite groups." MATEMATIKA 33, no. 1 (September 20, 2017): 87. http://dx.doi.org/10.11113/matematika.v33.n1.812.

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In this paper, we initiate the study of spectrum of the commuting graphs of finite non-abelian groups. We first compute the spectrum of this graph for several classes of finite groups, in particular AC-groups. We show that the commuting graphs of finite non-abelian AC-groups are integral. We also show that the commuting graph of a finite non-abelian group G is integral if G is not isomorphic to the symmetric group of degree 4 and the commuting graph of G is planar. Further, it is shown that the commuting graph of G is integral if its commuting graph is toroidal.
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Ahmadidelir, Karim. "On the non-commuting graph in finite Moufang loops." Journal of Algebra and Its Applications 17, no. 04 (April 2018): 1850070. http://dx.doi.org/10.1142/s0219498818500706.

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The non-commuting graph associated to a non-abelian group [Formula: see text], [Formula: see text], is a graph with vertex set [Formula: see text] where distinct non-central elements [Formula: see text] and [Formula: see text] of [Formula: see text] are joined by an edge if and only if [Formula: see text]. The non-commuting graph of a non-abelian finite group has received some attention in existing literature. Recently, many authors have studied the non-commuting graph associated to a non-abelian group. In particular, the authors put forward the following conjectures: Conjecture 1. Let [Formula: see text] and [Formula: see text] be two non-abelian finite groups such that [Formula: see text]. Then [Formula: see text]. Conjecture 2 (AAM’s Conjecture). Let [Formula: see text] be a finite non-abelian simple group and [Formula: see text] be a group such that [Formula: see text]. Then [Formula: see text]. Some authors have proved the first conjecture for some classes of groups (specially for all finite simple groups and non-abelian nilpotent groups with irregular isomorphic non-commuting graphs) but in [Moghaddamfar, About noncommuting graphs, Sib. Math. J. 47(5) (2006) 911–914], Moghaddamfar has shown that it is not true in general with some counterexamples to this conjecture. On the other hand, Solomon and Woldar proved the second conjecture, in [R. Solomon and A. Woldar, Simple groups are characterized by their non-commuting graph, J. Group Theory 16 (2013) 793–824]. In this paper, we will define the same concept for a finite non-commutative Moufang loop [Formula: see text] and try to characterize some finite non-commutative Moufang loops with their non-commuting graph. Particularly, we obtain examples of finite non-associative Moufang loops and finite associative Moufang loops (groups) of the same order which have isomorphic non-commuting graphs. Also, we will obtain some results related to the non-commuting graph of a finite non-commutative Moufang loop. Finally, we give a conjecture stating that the above result is true for all finite simple Moufang loops.
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Dissertations / Theses on the topic "Non-isomorphic graph"

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Badar, Muhammad, and Ansir Iqbal. "Polya's Enumeration Theorem : Number of colorings of n-gons and non isomorphic graphs." Thesis, Linnaeus University, School of Computer Science, Physics and Mathematics, 2010. http://urn.kb.se/resolve?urn=urn:nbn:se:lnu:diva-6199.

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Polya’s theorem can be used to enumerate objects under permutation groups. Using grouptheory, combinatorics and some examples, Polya’s theorem and Burnside’s lemma arederived. The examples used are a square, pentagon, hexagon and heptagon under theirrespective dihedral groups. Generalization using more permutations and applications tograph theory.Using Polya’s Enumeration theorem, Harary and Palmer [5] give a function whichgives the number of unlabeled graphs n vertices and m edges. We present their work andthe necessary background knowledge.

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Bird, William Herbert. "Graph Distinguishability and the Generation of Non-Isomorphic Labellings." Thesis, 2013. http://hdl.handle.net/1828/4839.

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A distinguishing colouring of a graph G is a labelling of the vertices of G with colours such that no non-trivial automorphism of G preserves all colours. The distinguishing number of G is the minimum number of colours in a distinguishing colouring. This thesis presents a survey of the history of distinguishing colouring problems and proves new bounds and computational results about distinguishability. An algorithm to generate all labellings of a graph up to isomorphism is presented and compared to a previously published algorithm. The new algorithm is shown to have performance competitive with the existing algorithm, as well as being able to process automorphism groups far larger than the previous limit. A specialization of the algorithm is used to generate all minimal distinguishing colourings of a set of graphs with large automorphism groups and compute their distinguishing numbers.
Graduate
0984
0405
bbird@uvic.ca
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Liu, Yi-Jin, and 呂宜錦. "The Interchange Graphs of Non-isomorphic Tournaments with Minimum Score Vectors Are Exactly Hypercubes." Thesis, 2011. http://ndltd.ncl.edu.tw/handle/35478602496317352048.

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碩士
國立臺北商業技術學院
資訊與決策科學研究所
99
A tournament of size n, denoted by Tn, represents the players p1,p2,...,pn in a round robin tournament and every two distinct players pi and pj compete exactly one game to decide the winner (and the loser) between them and tie is not permitted. If pi beats pj, we write pi→pj. The score of a player pi in a tournament, denoted si, is the number of players beaten by pi, and the score sequence of Tn is a non-decreasing order list of scores of all players, denote by Sn=(s1,s2,...,sn). Let T(Sn) be the collection of tournaments that realize a given score sequence Sn. A tournament is called strong if there exist directed paths for each of a pair of vertices. A score sequence Sn is said to be strong if there is a strong tournament in T(Sn). In a strong tournament Tn with score sequence Sn=(s1,s2,...,sn), Moon shows that there has exactly C(n,3)-Σ(i=1 to n)C(si,2) (directed) cycles of length 3, for short a 3-cycles. A △-interchange is a transformation which reverses the orientations of the arcs in the 3-cycle of a tournament. An interchange graph is an undirected graph whose vertices are the tournaments in T(Sn) and an edge joins two vertices (tournaments) if they can be transformed to each other by a △-interchange. Chen et al., in 2009, shown that the interchange graphs of tournaments with score sequence Ŝn=(1,1,2,...,n-3,n-2,n-2) are hypercubes with dimension n-2. They studied in the case when the vertices of the tournaments were labeled. If the label removed, some of the tournaments can be regarded as the same. In general, two tournaments are said to be isomorphic if there is a one-to-one correspondence between their vertices and edges such that incidences are preserved. In this thesis, we prove that the interchange graph of non-isomorphic tournaments with the same score sequence Ŝn can be hypercube Qn-4.
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Book chapters on the topic "Non-isomorphic graph"

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Mhiri, Islem, Ahmed Nebli, Mohamed Ali Mahjoub, and Islem Rekik. "Non-isomorphic Inter-modality Graph Alignment and Synthesis for Holistic Brain Mapping." In Lecture Notes in Computer Science, 203–15. Cham: Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-78191-0_16.

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Tran, Dat Hoang, and Ryuhei Uehara. "Efficient Enumeration of Non-isomorphic Ptolemaic Graphs." In WALCOM: Algorithms and Computation, 296–307. Cham: Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-39881-1_25.

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Chakraborty, Maumita, Sumon Chowdhury, and Rajat Kumar Pal. "Generation of Simple, Connected, Non-isomorphic Random Graphs." In Advances in Intelligent Systems and Computing, 69–77. Singapore: Springer Singapore, 2019. http://dx.doi.org/10.1007/978-981-13-8962-7_6.

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Yamazaki, Kazuaki, Mengze Qian, and Ryuhei Uehara. "Efficient Enumeration of Non-isomorphic Distance-Hereditary Graphs and Ptolemaic Graphs." In WALCOM: Algorithms and Computation, 284–95. Cham: Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-68211-8_23.

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Géraud, Rémi, Mirko Koscina, Paul Lenczner, David Naccache, and David Saulpic. "Generating Functionally Equivalent Programs Having Non-isomorphic Control-Flow Graphs." In Secure IT Systems, 265–79. Cham: Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-70290-2_16.

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Jayawardene, Chula J. "Tripartite and Quadpartite Size Ramsey Numbers for All Pairs of Connected Graphs on Four Vertices." In Handbook of Research on Advanced Applications of Graph Theory in Modern Society, 251–66. IGI Global, 2020. http://dx.doi.org/10.4018/978-1-5225-9380-5.ch010.

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A popular area of graph theory is based on a paper written in 1930 by F. P. Ramsey titled “On a Problem on Formal Logic.” A theorem which was proved in his paper triggered the study of modern Ramsey theory. However, his premature death at the young age of 26 hindered the development of this area of study at the initial stages. The balanced size multipartite Ramsey number mj (H,G) is defined as the smallest positive number s such that Kj×s→ (H,G). There are 36 pairs of (H, G), when H, G represent connected graphs on four vertices (as there are only 6 non-isomorphic connected graphs on four vertices). In this chapter, the authors find mj (H, G) exhaustively for all such pairs in the tripartite case j=3, and in the quadpartite case j=4, excluding the case m4 (K4,K4). In this case, the only known result is that m4 (K4,K4) is greater than or equal to 4, since no upper bound has been found as yet.
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"Selberg's Trace Formula and Isospectral Non-isomorphic Graphs." In Fourier Analysis on Finite Groups and Applications, 385–93. Cambridge University Press, 1999. http://dx.doi.org/10.1017/cbo9780511626265.025.

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Conference papers on the topic "Non-isomorphic graph"

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Alumbaugh, John Calvin, Qinghua Li, and Vincent Hu. "Differentiating Non-Isomorphic Graphlets for Graph Analytics." In 2016 IEEE 2nd International Conference on Collaboration and Internet Computing (CIC). IEEE, 2016. http://dx.doi.org/10.1109/cic.2016.053.

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Zhou, Kaixiong, Qingquan Song, Xiao Huang, Daochen Zha, Na Zou, and Xia Hu. "Multi-Channel Graph Neural Networks." In Twenty-Ninth International Joint Conference on Artificial Intelligence and Seventeenth Pacific Rim International Conference on Artificial Intelligence {IJCAI-PRICAI-20}. California: International Joint Conferences on Artificial Intelligence Organization, 2020. http://dx.doi.org/10.24963/ijcai.2020/188.

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The classification of graph-structured data has be-come increasingly crucial in many disciplines. It has been observed that the implicit or explicit hierarchical community structures preserved in real-world graphs could be useful for downstream classification applications. A straightforward way to leverage the hierarchical structure is to make use the pooling algorithms to cluster nodes into fixed groups, and shrink the input graph layer by layer to learn the pooled graphs.However, the pool shrinking discards the graph details to make it hard to distinguish two non-isomorphic graphs, and the fixed clustering ignores the inherent multiple characteristics of nodes. To compensate the shrinking loss and learn the various nodes’ characteristics, we propose the multi-channel graph neural networks (MuchGNN). Motivated by the underlying mechanisms developed in convolutional neural networks, we define the tailored graph convolutions to learn a series of graph channels at each layer, and shrink the graphs hierarchically to en-code the pooled structures. Experimental results on real-world datasets demonstrate the superiority of MuchGNN over the state-of-the-art methods.
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Jonnalagadda, Srinath, and Sundar Krishnamurty. "Modified Standard Codes in Enumeration and Automatic Sketching of Mechanisms." In ASME 1996 Design Engineering Technical Conferences and Computers in Engineering Conference. American Society of Mechanical Engineers, 1996. http://dx.doi.org/10.1115/96-detc/mech-1192.

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Abstract This paper presents the application of modified standard codes in the systematic enumeration and graphical display of non-isomorphic mechanisms. A two-stage enumeration procedure is presented that involves the identification and generation of contracted graphs using modified standard codes. In this scheme, unique numbering reflecting the symmetry properties of the higher order links deduced from these contracted graphs is propagated to the second stage in which all the non-isomorphic kinematic chains corresponding to each contracted graph are enumerated. The integration of the resulting numerical code values with a robust automatic sketching algorithm provides the basis for the systematic enumeration and pictorial displays of basic kinematic chains. Illustrative examples from the enumeration of basic kinematic chains with up to 12 bar 3 degree of freedom system are presented, and the results are discussed.
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Huang, Jing, and Jie Yang. "UniGNN: a Unified Framework for Graph and Hypergraph Neural Networks." In Thirtieth International Joint Conference on Artificial Intelligence {IJCAI-21}. California: International Joint Conferences on Artificial Intelligence Organization, 2021. http://dx.doi.org/10.24963/ijcai.2021/353.

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Hypergraph, an expressive structure with flexibility to model the higher-order correlations among entities, has recently attracted increasing attention from various research domains. Despite the success of Graph Neural Networks (GNNs) for graph representation learning, how to adapt the powerful GNN-variants directly into hypergraphs remains a challenging problem. In this paper, we propose UniGNN, a unified framework for interpreting the message passing process in graph and hypergraph neural networks, which can generalize general GNN models into hypergraphs. In this framework, meticulously-designed architectures aiming to deepen GNNs can also be incorporated into hypergraphs with the least effort. Extensive experiments have been conducted to demonstrate the effectiveness of UniGNN on multiple real-world datasets, which outperform the state-of-the-art approaches with a large margin. Especially for the DBLP dataset, we increase the accuracy from 77.4% to 88.8% in the semi-supervised hypernode classification task. We further prove that the proposed message-passing based UniGNN models are at most as powerful as the 1-dimensional Generalized Weisfeiler-Leman (1-GWL) algorithm in terms of distinguishing non-isomorphic hypergraphs. Our code is available at https://github.com/OneForward/UniGNN.
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Sunkari, Rajesh Pavan, and Linda C. Schmidt. "Laplace and Extended Adjacency Matrices for Isomorphism Detection of Kinematic Chains Using the Characteristic Polynomial Approach." In ASME 2005 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2005. http://dx.doi.org/10.1115/detc2005-84609.

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The kinematic chain isomorphism problem is one of the most challenging problems facing mechanism researchers. Methods using the spectral properties, characteristic polynomial and eigenvectors, of the graph related matrices were developed in literature for isomorphism detection. Detection of isomorphism using only the spectral properties corresponds to a polynomial time isomorphism detection algorithm. However, most of the methods used are either computationally inefficient or unreliable (i.e., failing to identify non-isomorphic chains). This work establishes the reliability of using the characteristic polynomial of the Laplace matrix for isomorphism detection of a kinematic chain. The Laplace matrix of a graph is used extensively in the field of algebraic graph theory for characterizing a graph using its spectral properties. The reliability in isomorphism detection of the characteristic polynomial of the Laplace matrix was comparable with that of the adjacency matrix. However, using the characteristic polynomials of both the matrices is superior to using either method alone. In search for a single matrix whose characteristic polynomial unfailingly detects isomorphism, novel matrices called the extended adjacency matrices are developed. The reliability of the characteristic polynomials of these matrices is established. One of the proposed extended adjacency matrices is shown to be the best graph matrix for isomorphism detection using the characteristic polynomial approach.
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Lucero, Briana M., and Matthew J. Adams. "Common Functionality Across Engineering Domains Through Transfer Functions and Bond Graphs." In ASME 2016 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2016. http://dx.doi.org/10.1115/detc2016-59769.

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Functional Modeling allows a direct, and sometimes abstract, method for depicting a product. Through this method, product architecture, concept generation and physical modeling can be used to obtain repeatable and more meaningful results. The Functional Basis approach of engineering design, as taught to engineering design students, provides the vocabulary to produce a uniform approach to function structures with functions (verbs) and flows (nouns). This paper suggests that the flows, particularly the “signal” flows, can be correlated to additional domains domain through transfer functions common in controls engineering. Controls engineering employs transfer functions to mathematically represent the physical or digital functions of a system or product using block diagrams to show the individual steps. The research herein suggests the correlations between the mathematical representations of transfer functions and the functional basis of engineering design through the actions performed upon “signal” flows. Specifically, the methodologies employed by controls engineering can relate to engineering design by 1) Schematic similarities, 2) Quantifiable performance metric inputs/outputs, 3) Mathematical representations of the flows, and 4) isomorphic matching of the schematics. Controls systems use block diagrams to represent the sequential steps of the system, These block diagrams parallel the functions structures of engineering design. Performance metrics between the two domains can be complimentary when decomposed down to non-dimensional engineering units. Mathematical Functions of the actions in a controls systems can resemble the functional basis functions through the use if bond graphs by identifying characteristic behavior of the functions on the flows. Isomorphic matching using the schematic diagrams can be used to find analogies based upon similar functionality and target performance metrics. When these four similarities are performed, parallels between the engineering domain and the controls engineering can be establish. Examples of cross-domain matching via transfer functions and controls systems are provided as contextualization for the concepts proposed. Pathways forward for this preliminary research are additionally suggested.
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