Her Mark
Rin had accepted Sesshoumaru. She loved him too. It was one of the few marvels in this world that genuinely astonished him. How could it not? He was not affectionate. Nor was he even human. Besides that, he had many other faults. But she did accept him, and Rin accepted him wholeheartedly.
When they had consummated that love, he had laid his mark upon her neck. He really liked that mark. It signified that acceptance, the love that they shared, and most importantly declared to any and all people (humans and demons alike) that she was his.
Rin was very beautiful. So Sesshoumaru wouldn't say that he was a possessive demon, he just killed anyone that touched what was his. It only happened once, and Rin hadn't spoke to him for days, so he learned to be less nonchalant about it. Thankfully, that one example seemed to ward off anymore males.
So actually, Sesshoumaru loved that mark. Not that he would ever let Rin know the reasons behind it. Nope, because even if he was a dog demon he definitely didn't like the dog house.