The Mathew line is direct from Terlion's (Tybion) son (Merion) (Merioneth), born 445 who came to North Wales with his Grandfather Cunedda being that his father had died before the invasion. Merioneth was the eldest son of Terlion the other son being Cadwaladr born abt. 450. After the invasion, Merioneth was given the land which was to be called Meirionydd.

Merioneth, born 445 in Scotland and King of Merioneth (As a reward for fighting with his grandfather in the invasion of North Wales, his grandfather Cunedda handed over to him, the area that became known as Meirionydd in his
honour.  The dynasty continued under the shadow of Gwynedd for several centuries.  The last King was apparently
killed fighting King Oswald of Northumbria on the Severn in 635. The land was called Cantrev Orddwys, the land of
Tstumaner.  Falling away from the league-long crest of Cader-Cader Idris down to the glittering sea between the Dyvi
and the Mawddach. Why is it called Meirionydd?  Meirion Meirionydd is Meirion's name in the genealogies of the
Princes. Meirionydd was culturally part of Powys, it became one of the vassal kingdoms to Gwynedd, through the sons of Cunedda, and although it retained its own dynasty for three centuries, it is not clear how independent it
remained.
        * Cadwaladr (Gadgulard), 475, next.
        * Bleiddud
        * Cadwallon
Cadwaladr (Catgualart), Meirionydd, born abt. 475, reigned 510s. The son of Meirion.  His reigned coincided with
that of Cadwallon Lawhir, to whom he was almost certainly a vassal.
        * Gwrin Varvdrwch (Gwrgant Farfdrwch), next
Gwrin Farfdrwch, (of the Ragged Beard), Meirionydd, born abt. 505, m. Marchell ferch Brychan.  This is the same king identified by Geoffrey of Monmouth as Gurguit Barbtruc, though he had displaced him to some time around 300BC.  Gurguit fought the Danes, chased them back to their home country and subdued them.  Gwrin may well have been a wise king but faced with considerable onslaught from his neighbours and from Irish priates.  It was during Gwrin's reign that St. Cadfan came to Wales and established churches at Tywyn and Bardsey.
Clydno (Glitnoth Garahnhir) (Longshanks), Meirionydd, born abt. 525. Reigned 570s.  Nothing is recorded of him in the annals, but it is possible he is treated by Geoffrey of Monmouth as Guithelin, a temperate and liberal king whose wife, Marcia, apparently developed an extensive Code of Laws subsequently used by King Alfred.
Gwyddno Garanhir, (Gueinoth), Meirionydd, born abt. 545. Reigned 600s.  A comtemporary and possibly a vassal king of Iago ap Beli of Gwynedd.  He was the father of Idris.
Idris Arw, Meirionydd, born abt. 565, died 632.  One of the few kings of Meirionydd whose name lives on in the dark and sinister mountain of Cader Idris, or Throne of Idris.  He may well have used Cader Idris as the site for a fort during the many battles and seiges that would have raged through Meirionydd at this time.  Idris's death is recorded in a battle on the banks of the river Severn in 632.
Sualda, (Swalda), Meirionydd, born abt. 595. Reigned 640s.  The son of Idris - nothing is recorded of Sualda's reign,
though it is contemporary with the rise to power of Cynddylan and we can imagine that Sualda served as a client king in Cynddylan's army.  He was succeeded by his son Brochmael.
Brochwel, (Brochmael), Meirionydd, born abt. 625. Died 662.  The succesor to Sualda, he was killed in battle in 662.  The Welsh annals confuse him with Brochfael Ysgythrog of Powys who lived a century earlier.
Einudd Bach
Ednyfed
    * Einon, next
    * Brochwel
Einon
Peredur Beiswrdd or (Beiswyn), born abt. 850, King of Ceredigion Uchaf. (Built Llys Peredur yNghaero and the church of Llanfchangel).
    * Cydifor, next
    * Pwyll
    * Pill
    * Gwylfyw
    * Edelfrych