How is the dramatic purpose of the ghost in Act 1 of Shakespeare's Hamlet to show the strong relationship between Hamlet and his father before he was murdered?

Let's go step by step. Reading through and considering the situations of each scene in Act 1 slowly explains to us the relationship between Hamlet and his father.
Firstly, we learn that the ghost of the dead King of Denmark has begun appearing to guards at night time. Each time, the guards try to speak to it and understand what it is and why it appears. But the ghost does not speak and does not respond to them. Horatio, a friend of Hamlet, says that they should inform Hamlet about this, for the ghost that refuses to speak to them shall surely speak to him. This is really the first indication we have as to the nature of the father-son relationship. Horatio, who knew the king well and who also knows Hamlet well, implies that the ghost of the King would not be silent upon seeing his son, indicating that Hamlet and his father had a strong bond before the King's death.
And then consider the entry of Hamlet in Act I, Scene II, when his mother Gertrude immediately criticizes Hamlet for continuing to mourn his father's death. His mother asks him to stop wearing black clothes, a sign of mourning, saying that he cannot continue to think of his father all his life... and that it's common for people to die.
Hamlet explains to his mother the extent of his grief and mourning, which is far deeper than what his dark clothes, weepy eyes and sighs show. This is the most significant moment when we realize that Hamlet's love and attachment for his father was very strong and deep, much deeper than what his mother or uncle had felt, as they have visibly moved on with their lives by getting married and advise Hamlet to do the same. But Hamlet is in deep grief over his father's death and also over the unexpected and quick marriage of his mother to his uncle. 
Hamlet goes on to meet Horatio and others in Scene II and speaks highly of his father, saying that he will not come across a man like his father again. 
And in Act I, Scene IV, the ghost of the King comes again and motions for Hamlet to follow him. The ghost then proceeds and speaks to Hamlet, telling him that he is the ghost of the King and asks him to revenge him, to which Hamlet immediately accepts. Then the ghost goes on to tell him that he was murdered by his uncle, asks him to take revenge and asks Hamlet to remember him. Hamlet is naturally devastated and vows to avenge his father and says that he will remember only his father.
So Hamlet's father only spoke to Hamlet and not only did he do so, but he revealed the secret of his death and also entrusted Hamlet to avenge his death. We understand from this scene that not only did Hamlet love his father very much, but that his father loved Hamlet a lot, too. The King clearly felt that only Hamlet was worthy and capable of the task of avenging his death and reached out to him as a ghost and not to anyone else. 
From all of these scenes, we understand that Hamlet and his father shared a most strong and deep bond of love and trust.