Do we generally store the degree of each vertex in the linked list implementation? if not, why? So generally speaking, when we implement the graph using linked list, do we store the degree of each edge too?

I'm asking this because if a question in my exam stated that we implemented this graph using linked list, do i assume we can access the degree of each edge in o(1) or not? this matters because it effects the time complexity of algorithms like finding if the graph has euler cycle which i should check the degree of each edge

and the exams are SAT type of questions so i can't write down anything i should just choose one of the 4 answers which for example says the time complexity of finding if the graph has euler path in linked list implementation
Normally we don't; the adjacency list representation is a list of out-edges, but doesn't separately store the degree.  However, you can certainly store that additional information if you want.  You can choose how you want to represent the graph, and it's not hard to modify the standard data structure to keep track of the out-degree of each vertex.