The original alphabet, which Graves concocts his ultimately highly flawed sprawling White Goddess tome with; is called Ogam.
It is named after the Tuatha De Dannan (people of the goddess Danu) god Ogma, son of Dagda, the chief deity of this mythological race, who were the sixth and penultimate race of supernatural beings to "take" the island as documented in the Lebor Gabála Érenn - The Book of the Takings of Ireland.
These were only in possession of the island for 300 years or so, before the final takers, the Milesians, who the founding bardic poet, Amergin, was the druid of, came and took it from them and banished the Tuatha De Dannan to beneath the hills and into the Sidhe mounds (phonetic 'shee'), where they became the sidhe or faeries of folklore.
This is an alphabet of originally 20 and later, post 8C twenty five letters, unique to Brythonic (now welsh) and Gaelic culture.
The alphabet was divided into four families or aicmes, of five letters, and each aicme took the name of it's first letter, and all the letters related to various trees. This is why it is called the tree alphabet. Ireland at the time of its invention was covered in trees. The sequence of this alphabet is:
B L F S N - H D T C Q - M G Ng Z R - A O U E I
You will notice that this is not in the roman order, and by analysing the arrangement we can discover the mathmatical formula the druids came up with to create ogam.
If we lay out the letters in their roman order we get 18 and the sounds V, pronounced as an F and Ng, were then tacked onto the end, so:
A B C D E G H I L M N O Q R S T U Z F Ng
What they did was separate out the vowels and group them into broad and slender, in the order:
A O U E I - this is the fourth and final sequence in the ogam alphabet and is called Aicme Ailme (original meaning of ailme unknown).
We then take out the early Irish names for the numerals one to five: H (huath) D (da) T (tri) C (cethair) Q (quic)
H D T C Q - this is the second family called: Aicme hÚatha (original meaning unknown)
This leaves us ten letters:
B G L M N R S Z F Ng
From this group we take every second letter, beginning with the B, giving us:
B L N S F - the first family: aicme beith/birch
The five letters left: G M R Z Ng, are then re-ordered, beginning with M, the letter in the middle at position 10 in the original group of twenty, and create the sequence working backwards.
This gives us the third family, aicme Muin (neck):
M G NG Z R
The three consonantal aicme/sets of letters, are then arranged in alphabetical order, the first letter in each group dictating where the aicme is placed, so aicme beith B goes first, then aicme hÚatha H, second, aicme muin M third and the vowels to end it. Thus giving the final order
B L N S F - H D T C Q - M G NG Z R - A O U E I
This cryptographic process seems perfectly in keeping with the Bardic love of mystery and concealment.
Each letter in the four aicme, has three kennings associated with them, preserved in three Bríatharogaim (word-ogam) lists, dating to the Old Irish period 5-7C, which can be viewed here