In mathematics, especially group theory, two elements a {\displaystyle a} and b {\displaystyle b} of a group are conjugate if there is an element g {\displaystyle g} in the group such that b = g a g − 1.
A conjugate acid, within the Brønsted–Lowry acid–base theory, is a chemical compound formed when an acid gives a proton to a base—in other words, it is a base with a hydrogen ion added to it, as it loses a hydrogen ion in the reverse reaction.
In the mathematical discipline of graph theory, the line graph of an undirected graph G is another graph L that represents the adjacencies between edges of G. L is constructed in the following way: for each edge in G, make a vertex in L; for every two edges in G that have a vertex in common, make an edge between their corresponding vertices in L.
In mathematics, the conjugate of an expression of the form a + b d {\displaystyle a+b{\sqrt {d}}} is a − b d, {\displaystyle a-b{\sqrt {d}},} provided that d {\displaystyle {\sqrt {d}}} does not appear in a and b.
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