A little history of Armenian contribution to Byzantine Empire.
Due to centuries of foreign domination, much of Armenian history has been neglected and surprised. As such much of the influence Armenians had on the Byzantine empire has been swept under the rug by the Ottomans and later the Soviets. Nevertheless the contributions of Armenian people to the Byzantine empire has been more than significant. As the historian P. Charanis (1959) says: “The important role played in the history of Byzantium by that talented minority, the Armenians, has been generally unrecognized.”
Even though Armenia was only in part a vessel of Byzantium, many Armenians became successful in the Byzantine Empire. From bishops, architects, important military figures and even Emperors, Armenians where represented in all walks of Byzantine life. In fact one out of five Byzantine emperors and empresses were ethnically full or in part Armenian.
Below is a list of over 20 Byzantine Emperors of Armenian origin in a chronological order.
1) Maurice (Latin: Flavius Mauricius Tiberius Augustus, Armenian: Morick Oshakanatsi), reign: (582 – 602 ) A.D.
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2) Philippikos Bardanes (Armenian: Vardan Pikick), reign: (711– 713) A.D.
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3) Artavasdos, (Latin: Artabasdos, Armenian: Artavazd), reign: (741 – 743) A.D.
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4) Leo V the Armenian (Armenian: Levon Artsruni), reign: (813 – 820) A.D
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5) Theodora (wife of Theophilos, Empress and regent of her son Michael III), reign: (829 – 867) A.D.
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6) Michael III (Armenian from the mothers side), reign: (842 – 876) A.D.
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7) Basil I (Armenian: Barseg Arsha), reign: (867 – 886) A.D.
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8 ) Leo VI the Philosopher (Armenian: Levon Arshakuni), reign: (886 – 912) A.D.
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9) Alexander, reign: (912 – 913) A.D.
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10) Constantine VII Porphyrogennetos (“the Purple-born”), reign: (913 – 959) A.D.
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11) Romanos I Lekapenos (Armenian: Romanos Vashtakian), reign: (920 – 944) A.D.
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12) Romanos II, reign: (959 – 963) A.D.
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13) Nikephoros II Phokas, reign: (963– 969) A.D.
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14) John I Tzimiskes (Armenian: Hovhannes Chmushkik, born of the Kourkouas clan), reign: (969 – 976) A.D.
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15) Basil II the Bulgar-slayer, reign: (976 – 1025) A.D.
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16) Constantine VIII, reign: (1025 – 1028) A.D.
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17) Romanos III Argyros, reign: (1028 – 1034) A.D.
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18) Michael IV the Paphlagonian, reign: (1034 – 1041) A.D.
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19) Michael V the Caulker, reign: (1041 – 1042) A.D.
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20) Constantine IX Monomachos, reign: (1042 – 1055) A.D.
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21) Theodora Porphyrogenita (Empress), reign: (1054 – 1056) A.D.
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22) Michael VI Stratiotikos, reign: (1056 – 1057) A.D.
Sources:
1) Illustrated Armenia and the Armenians – Page 58 by Ohan Gaidzakian (1898)
http://www.archive.org/stream/illustratedarmen00gaid#page/26/mode/2up
2) Wikipedia
3) http://www.armeniapedia.org/index.php?title=Byzantine_Empire
PeopleOfAr 
You’ve forgotten to add emperor Heraclius and his dynasty (more than 10 emperors of Armenian origins
true I’ve left out quit a number. I might do part 2, and also am planning to do a post on Armenian military figures of Byzantium. As is recorded Armenians made up the largest part of Byzantine military aristocracy, yet little written about it by modern historians.