Sri Mallikarjuna Swamy is one of the twelve Jyotirlingas of Lord Shiva situated at srisailam on Shri Shaila Mountain on the bank of Patal Ganga, Krishna River in the southern state of Andhra Pradesh.
According to Shiva Purana, when Shiva and Parvati decided to find suitable brides for their sons Ganesha and kartikeya argued as to who is to get wedded first .Lord Shiva bade that the one who goes round the world in Pradakshinam could get married first. By the time Lord Kartikeya could go round the world on his vahana, Lord Ganesha went round his parents 7 times (for according to Shastras, going in pradakshinam round one’s parents is equivalent to going once round the world (Bhupradakshinam).
So Lord Ganesh was married of before his brother Kartikeya, kartikeya on his return was enraged and went away to stay alone on Kraunch Mountain in the name of Kumarabrahmachari. Despite being stopped and consoled by his parents Shiv-Parvati, Kartikeya went away to the Kraunch Mountain. Even the Gods went and tried consoling Kartikeya but all their efforts were in vain. Because of this incident Shiv-Parvati were very sad and both decided that they would themselves go to Kraunch Mountain.
On seeing his father coming over to pacify him, he tried to move to another place, Eventually Lord Shiva assumed the form of Jyotirlinga and resided on that mountain by the name of Mallikarjuna. Mallika means Parvati, while Arjuna is another name of Shiva. In this way both Shiva and Parvati came to reside in this linga. The place where Lord Siva and Parvati stayed came to be known as Shrishailam. Lord Siva visits Lord Kartikeya on Amavasya day & Parvati Devi on Poornima