I have heard two explanations of 'Devasenapati' as an adjective of Lord Kartikeya.
He is the husband of DevasenA, ie 'DevasenA-pati'.
He is the Chief of the Divine Army, ie 'Deva-senApati'.
Which one is supported by the scriptures?
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Both the meaning are supported by scriptures.
Story of Devasena is said in Vanaparva of Mahabharata by sage Markandeya to Yudhishtira. She is daughter of Prajapati. She was rescued by Indra from asura Kesin. After saving her from the Asura, he inquired who she is and she introduces herself.
"The lady replied, 'I am a daughter of Prajapati (the lord of all creatures, Brahma*) and my name is Devasena. My sister Daityasena has ere this been ravished by Kesin. We two sisters with our maids habitually used to come to these Manasa mountains for pleasures with the permission of Prajapati. And the great Asura Kesin used daily to pay his court to us. Daityasena, O conqueror of Paka, listened to him, but I did not. Daityasena was, therefore, taken away by him, but, O illustrious one, thou hast rescued me with thy might. And now, O lord of the celestials, I desire that thou shouldst select an invincible husband for me.' To this Indra replied, 'Thou art a cousin of mine, thy mother being a sister of my mother Dakshayani, and now I desire to hear thee relate thine own prowess.' The lady replied, 'O hero with long arms, I am Avala (weak) but my husband must be powerful. And by the potency of my father's boon, he will be respected by gods and Asuras alike.' Indra said, 'O blameless creature, I wish to hear from thee, what sort of power thou wishest thy husband to possess.' The lady replied, 'That manly and famous and powerful being devoted to Brahma, who is able to conquer all the celestials, Asuras, Yakshas, Kinnaras, Uragas, Rakshasas, and the evil-minded Daityas and to subdue all the worlds with thee, shall be my husband.'
Listening to this description, Indra thought there is none who could match the requirements of the lady and saw some astrological signs indicating fearful war in coming future. He thought that a person born at that moment could be a suitable bridegroom for the lady. When this was happening, a war between devas and Asuras was taking place. He thought of possibilities that a son is born through devas and reached Brahma.
This union of the Moon (Soma) with the Sun and Agni is very wonderful. And if Soma giveth birth to a son now, that son may become the husband of this lady. And Agni also hath similar surroundings now, and he too is a god. If the two begetteth a son, that son, may become the husband of this lady.' With these thoughts that illustrious celestial repaired to the regions of Brahma, taking Devasena 1 with him. And saluting the Grandsire he said unto him, 'Do thou fix a renowned warrior as husband of this lady.'
Brahma replied as following:
Brahma replied, 'O slayer of Asuras, it shall be; as thou hast intended. The issue of that union will be mighty and powerful accordingly. That powerful being will be the husband of this lady and the joint leader of thy forces with thee.'
After he was announced as the leader of the army of devas, marriage between Skanda and Devasena was done (emphasis mine).
"The Performer of a thousand sacrifices then thought of Devasena, whom he has rescued before. And considering that this being (Skanda) was undoubtedly destined to be the husband of this lady by Brahma himself, he had her brought there, dressed her with the best apparel. And the vanquisher of Vala then said to Skanda, 'O foremost of gods, this lady was, even before thy birth, destined to be thy bride by that Self-existent Being. 1 Therefore do thou duly accept her lotus-like beautiful right hand with invocation of the (marital) hymns.' Thus told, he duly married her. And Vrihaspati learned in hymns performed the necessary prayers and oblations. She who is called Shashthi, Lakshmi, Asa, Sukhaprada, Sinivali, Kuhu, Saivritti, and Aparajita, is known among men as Devasena, the wife of Skanda. When Skanda became united to Devasena in indissoluble bonds of matrimony, then the gods of prosperity in her own personal embodiment began to serve him with diligence. As Skanda attained celebrity on the fifth lunar day, that day is called Sripanchami (or the auspicious fifth day) and as he attained his object on the sixth, that lunar day is considered to be of great moment.
Chapter 223, Vana Parva, Mahabharata translated by K.M Ganguli.
* It is translator's addition that Prajapati is Lord Brahma. Neither the Sanskrit verses nor other translators like Manmatha Nath Dutt directly mention Brahma
Indra and the devatas were in the need of a mighty being who could help them and lead them in the war with Asuras (It was King Muchukunda who helped devas in war before Kartikeya was born). After looking at the astrological signs, Indra was anticipating a war in coming future. He thought that the moment would be very energetic and wanted a being to be born from Devas. But after a turn of events, the born being was Kartikeya. After he was born, he destroyed the Krauncha hill with his prowess. At first, all think that he was an evil being and ask Indra to kill him but Indra recognizing his prowess and does not fight with him. (Vishwamitra was the first one to know that Skanda was born for a cause and worshipped him. He performed the ceremonies which are done to a child. Hence he became Kartikeya's favorite). Since he is powerful, gained followers and dispelled fears of the devatas and others within a very short time of six days, maharshis and Indra revered him and asked him to be their leader and ascend the throne of Indra. To this Skanda asks what are the duties of being an Indra (I explain in this answer). He does not seek sovereignty over Indra and agrees to be his servant. At the request of Lord Indra, he becomes the commander in chief of army.
Skanda replied, 'Thou, O Sakra, art my sovereign, as also of the three worlds; mayst thou be prosperous! Tell me if I can obey any commands of thine.'
Indra replied, 'At thy bidding, O powerful being, I shall continue to act as Indra. And if thou hast said this deliberately and in earnest, then hear me how thou canst gratify thy desire of serving me. Do thou, O mighty being, take the leadership of the celestial forces accordingly.'
Skanda replied, 'Do thou anoint me as leader, for the destruction of the Danavas, for the good of the celestials, and for the well-being of cows and Brahmanas.'
Markandeya continued, "Thus anointed by Indra and all other gods, and honoured by the Maharshis, he looked grand at the moment. The golden umbrella 1 held (over his head) looked like a halo of blazing fire. That famous god, the Conqueror of Tripura, himself fastened the celestial wreath of gold, of Viswakarma's manufacture, round his neck.
Chapter 228, Vana Parva, Mahabharata, translated by K.M Ganguli
Hence, it is also true that he is called the chief of army of Devatas.
Both the meanings apply to Kartikeya.