What is the relationship between Trysdale and the other character of the story

The question is from "The Cactus" by O. Henry. Trysdale is the main character in the story. There are two other characters, a woman Trysdale proposes to and the woman's brother who is also Trysdale's friend.

Explanation:

The Cactus by O. Henry is a story about how ego, hubris and dishonesty get in the way of one's happiness. The story is set in Trysdale's drawing room after the marriage ceremony of this girl was over and the scent of the huge bunches of flowers piled in the church was still haunting him.

Trysdale, a young man, noble, wealthy and cultured, realizes that his girl friend is excessively devoted to him and sort of worships him. 'She had always insisted on placing him upon a pedestal, and he had accepted her homage with royal dignity'.

Ultimately the day comes when Trysdale proposes to her. The girl is absolutely delighted at the proposal but shyly and modestly replies that she'll think about it. Trysdale eagerly waits for her answer. The next day, he receives a cactus with a tag in Spanish. Without trying to understand what it meant, he perceives this as rejection.

Now, as Trysdale returns from his ex-girlfriend's wedding, he is filled with bitterness. Trysdale was deeply distressed and looked unhappy. His friend, the bride's brother, coincidentally finds the tag on the cactus and tells him that the word on the tag was a common Spanish word that translated to the phrase, "Come and take me."

Trysdale now realizes his fault at ignoring the tag. He remembers lying to his girlfriend that he was fluent in Spanish whereas all his Spanish was mugged up from hackneyed Spanish phrases which he often learnt from the dictionaries and used them only to show off. Trysdale realizes that his dishonesty about the Spanish and his ego in not understanding the tag had cost him his happiness.