Distributed algorithms - $\alpha, \beta$ synchronizers
Please find solutions of all cases:

For case A ($\alpha$-synchronizer), the pulse at a node can either be more, equal, or less by one (therefore, $\{26,27,28\}$). This is because a node must inform its neighbors about its safeness and not all the other nodes (according to your question). 

You can see the rules in the following (copy-pasted from the paper)


A new pulse may be generated at a node whenever it is guaranteed that no
message sent at the previous pulses of the synchronous algorithm may arrive at
that node in the future. 
Using the acknowledgment mechanism described above, each
node detects eventually that it is safe and then reports this fact directly to all its neighbors. Whenever a node learns that all its neighbors are safe, a new pulse is generated.


For case B: ($\beta$-synchrnoizer) - if $v$ is the root, then at $v'$ the pulse is either the same or less (therefore, $\{26,27\}$). 

For case C: ($\beta$-synchrnoizer) - if both $v$ and $v'$ are leaves, then here we may assume that the broadcast of the root is not received at the same time - since the network is asynchronous (otherwise, why would we need a synchrnoizer). Here, if $v$ is 27 then $v'$ is either 28 if the update of $v'$ is received before $v$ ,, or 26 if the update of $v'$ is received after. Or they both have the same pulse  (therefore, the range is $\{26,27,28\}$.