The Van Halen frontman lost his battle with cancer on Oct. 6
On Friday, Wolf, 29, took to Instagram to post a black-and-white photo with his father, alongside a touching caption. The image, which appeared to be a selfie, showed the two beaming with bright smiles as they posed for the lens.
"1 month," he captioned the pic. "Not a second goes by where you’re not on my mind."
"I miss talking with you," continued Wolf, who replaced Van Halen bassist Michael Anthony in 2006. "I miss laughing with you. I miss listening to music with you. I miss making music with you. I just miss everything. I love you so much, Pop. It’s really hard being here without you."
Wolf was the one to share the sad news of Eddie's death on Twitter, calling him the "best father" and describing the moments he shared on stage with his dad as "a gift."
While some have speculated about Wolf taking Eddie's place in Van Halen, he has declared such claims "a shi**y lie."
He spoke up after a member of a fan page on social media posted a potential line-up for the band with Wolf as guitarist.
"This is just a shi**y lie attempting to capitalize on these awful times," Wolf responded. "Please stop with this. Anyone peddling this shit is not only hurting the fans, but hurting me and my family."
See more Eddie's death below.