Jesus specifically quoted the link of loving Him and obeying Him in John 14:15-16,21,23-24 when He said: "If you love Me, obey My commandments. And I will ask the Father, and He will give you another Counselor, who will never leave you".
"Those who obey My commandments are the ones who love Me. And because they love Me, My Father will love them, and I will love them. And I will reveal Myself to each one of them."
"And those who love Me will do what I say. My Father will love them, and We will come to them and live with them. Anyone who doesn't love Me will not do what i say.And remember, My words are not My own. This message is from the Father who sent Me."
And in John13:34,Jesus said, "A new command I give you:Love one another. As I have loved you, so you must love one another."
Thus, if we truly love Jesus, our Lord we prove it by our actions of obeying His new command.
It is so easy to tell other people we love them but not easy to show in our actions. It is the same way with God. Jesus who became man understood this that it why He wants us to "walk the talk" and not "talk the walk."