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Invariant Graph Partition Comparison Measures [PDF]
Symmetry, 2018 Symmetric graphs have non-trivial automorphism groups. This article starts with the proof that all partition comparison measures we have found in the literature fail on symmetric graphs, because they are not invariant with regard to the graph ...
Geyer-Schulz Andreas
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International Journal of Computer Mathematics, 1995
An E-graph is constructed by replacing each edge in a core graph G with a copy of a graph H. An important property of E-graphs is that their invariant values can be determined from parameters of the original graphs G and H. We determine chromatic number, clique number, vertex and edge cover numbers, vertex and edge independence numbers, circumference ...
Teresa W. Haynes, Linda M. Lawson
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An E-graph is constructed by replacing each edge in a core graph G with a copy of a graph H. An important property of E-graphs is that their invariant values can be determined from parameters of the original graphs G and H. We determine chromatic number, clique number, vertex and edge cover numbers, vertex and edge independence numbers, circumference ...
Teresa W. Haynes, Linda M. Lawson
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Discrete Mathematics, 2019
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Brian Alspach +2 more
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Brian Alspach +2 more
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IDEA: Invariant defense for graph adversarial robustness [PDF]
Information SciencesDespite the success of graph neural networks (GNNs), their vulnerability to adversarial attacks poses tremendous challenges for practical applications.
Shuchang Tao, Qi Cao, Yunfan Wu
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Transactions of the American Mathematical Society, 1991
The development of oriented and semioriented algebraic invariants associated to a class of embeddings of regular four valent graphs is given. These generalize the analogous invariants for classical knots and links, can be determined from them by means of a weighted averaging process, and define them by means of a new state model.
Jonish, D., Millett, K. C.
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The development of oriented and semioriented algebraic invariants associated to a class of embeddings of regular four valent graphs is given. These generalize the analogous invariants for classical knots and links, can be determined from them by means of a weighted averaging process, and define them by means of a new state model.
Jonish, D., Millett, K. C.
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Journal of Knot Theory and Its Ramifications, 2000
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Graphs and Combinatorics, 2002
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An Invariant of the Graph Isomorphism
2008 IEEE Pacific-Asia Workshop on Computational Intelligence and Industrial Application, 2008The adjacent matrix is defined in this paper for a given graph, and the deformation called dual congruent act on the matrix is discussed. We have shown that any two graphs are isomorphic each other if and only if they having the dual congruent adjacent matrices. So the adjacent matrix of graph is a isomorphic invariants for graph theory.
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