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4 - Cordial Labeling of Some Ladder and Book related Graphs
Published in N. P. Shrimali, Nita H. Shah, Recent Advancements in Graph Theory, 2020
Neha B. Rathod, Kailas K. Kanani
A-cordial labeling was introduced by Mark Hovey. He introduced A -cordial labeling for an abelian group as a simultaneous generalization of cordial and harmonious labeling. If A = V4, it is known as V4 -cordial labeling. Let V4 be the Klein-four group. In this chapter we prove some ladder and book related graphs which admit V4 -cordial labeling. We prove that Book Graph B(5, n), Mobius Ladder Mn Open Ladder O(Ln) and Mongolian Tent MT(2, n) are V4 -cordial graphs.
Elementary Algebra
Published in Dan Zwillinger, CRC Standard Mathematical Tables and Formulas, 2018
Subgroupsorder 4: 1, a, a2, a3order 2: 1, a2V , the Klein four group
Edge counts for the auxiliary pair graph within the graphical unitary group approach
Published in Molecular Physics, 2021
Table 4 lists the permutations among the 16 segment shapes produced by the symmetry operators. The set of all symmetry operators together with operator algebra is the Klein four-group. Equivalence relations on the set of all segment shapes can be defined using subgroups of V: if there exists an operator in the subgroup that relates one shape to another then the shapes are equivalent. Each equivalence relation partitions the segment shapes into equivalence classes; the equivalence class of shape x is . If then each shape is in a distinct equivalence class. If then there are 10 equivalence classes: 4 singletons, where , and 6 doubletons. If then there are also 10 equivalence classes: 4 singletons, where , and 6 doubletons. If then there are seven equivalence classes: two singletons, where , three doubletons, and two classes of cardinality four. Table 4 is ordered by ascending equivalence class size for the equivalence relation with empty lines separating the classes.