Thank you for the reply Old Smokey.
The textbook was definately trying to show that Vmu is inversely proportional to density as an IAS , because the graph it self had altitude and/or temp Vs IAS and its effect on Vmu and some other speeds . Even though the graph itself had no values , the slope of the Vmu line was significant enough to assume that density variations have a definate effect on Vmu . Unfortunately there is no explanation about this and basically any further reference to Vmu stops there. I dont even recall our intsructor commenting on that when i was doing the ATPLs.
Basically the textbook is the one by Oxford aviation training , book 6 , page 13-10 , ( just mentioning it in case you happen to have it , or any one else that reads this post )
Now with regard to EAS , i understand your point , but as you said this is nit-picking .
Im considering an indirect way in which density may affect Vmu.... Since Vmu occurs at the most nose-up attitute that the aeroplane can achieve , thrust will have a substantial vertical vector , so the higher the density , the more thrust , the more this vertical component will be , the less the Vmu .
just a thought basically.