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Graph Algorithms II
Published in R. Balakrishnan, Sriraman Sridharan, Discrete Mathematics, 2019
R. Balakrishnan, Sriraman Sridharan
Let us recall the operation of symmetric differencesymmetric difference of two sets: For any two sets A and B, the symmetric differencesymmetric difference of A and B denoted by AΔB is the set (A∪B)∖(A∩B) which is also equal to (A∖B)∪(B∖A).
Discrete Mathematics
Published in Dan Zwillinger, CRC Standard Mathematical Tables and Formulas, 2018
A⊆B⇔CB⊇CA. $$ A \subseteq B~ \Leftrightarrow ~CB \supseteq CA. $$ The symmetric difference of two sets A and B (represented as A ⊕ B or AB) is the set of elements that are in A or B and are not in both A and B (i.e., the union minus the intersection).
Elements of topology and homology
Published in Rodrigo Rojas Moraleda, Nektarios A. Valous, Wei Xiong, Niels Halama, Computational Topology for Biomedical Image and Data Analysis, 2019
Rodrigo Rojas Moraleda, Nektarios A. Valous, Wei Xiong, Niels Halama
Symmetric difference The addition operator on a vector space over the field Z2 is called the symmetric difference denoted by ⊕ (Table 1.1).
The 2-good-neighbour diagnosability of modified bubble-sort graphs under the PMC and MM* model
Published in Systems Science & Control Engineering, 2020
Let be an undirected simple graph and be a nonempty vertex subset of G. The induced subgraph is the graph whose vertex set is S and the edge set is the set of all the edges of G with both endpoints in S. The degree of a vertex is the number of edges incident to the vertex, with loops counted twice. The minimum degree of vertices in G is denote by . For any vertex v, is the neighbourhood of v in G which is the set of vertices adjacent to v. u is called a neighbour vertex of v when . We use to denote the set . A vertex cut of a connected graph G is a set of vertices whose removal renders G disconnected. The vertex connectivity is the size of a minimal vertex cut. A closed trail whose origin and internal vertices are distinct is a cycle. A cycle of length k is called a k-cycle. For two vertex sets and , a symmetric difference is a set of elements that belong to one set but not the other. A faulty set is called a g-good-neighbour faulty set if for every vertex . A g-good-neighbour cut of a graph G is a g-good-neighbour faulty set F such that G−F is disconnected. The minimum cardinality of g-good-neighbour cuts is said to be the -connectivity of G, denoted by . For graph-theoretical terminology and notations do not defined here we follow Bondy and Murty (2007).