حَمْدِ

A word in the Arabic language will either be 1) a verb or 2) a noun or 3) a particle – حَمْدِ is a noun

A noun may either be 1) Definite or indefinite 2) Masculine or feminine 3) Singular, dual or plural 4) Nominative, accusative or genitive

الحَمْدُ is the natural state of a definite noun and becomes الحَمْدِ due to: 1) a preposition that precedes it or 2) a possessed noun that precedes it

الحَمْدِ loses it’s definite article, becoming حَمْدِ due to it being a possessed noun

To praise, admire, thank, honor, magnify

Grammatical analysis of حَمْدِ
اسْمٌ مَجْرُوْرٌ بِالكَسْرَةِ الزَّاهِرَةِ وَهُوَ مُضَافٌ 
الْمَعْرِفَةُمُفْرَدٌمُذَكَّرٌمَجْرُوْرٌح م دبَاب سَمْعَحَمِدَ يَحْمَدُفَعْلٌاسْمٌالْمَصْدَرُ
DefiniteSingularMasculineGenitiveRootPraiseسPatternNounVerbal noun
Surah/Below are the 15 verses in the holy Quran containing the genitive, possessed nounحَمْدِ
Verse
And when your Lord said to the angels “Verily I am going to place a vicegerent on earth,”وَإِذْ قَالَ رَبُّكَ لِلْمَلَائِكَةِ إِنِّي جَاعِلٌ فِي الأَرْضِ خَلِيْفَةً
they said “will you place in it one who will make mischief therein and shed blood?قَالُوْا أَتَجْعَلُ فِيْهَا مَنْ يُفْسِدُ فِيْهَا وَيَسْفِكُ الْدِّمَآءَ
while we glorify You with Your praises and sanctify You”وَنَحْنُ نُسَبِّحُ بِحَمْدِكَ وَنُقَدِّسُ لَكَ
2-30He said “Truly I know that which you do not know”قَالَ إِنِّي أَعْلَمُ مَا لَا تَعْلَمُوْنَ
13-13
15-98
17-44
17-52
20-130
25-58
32-15
39-75
40-7
40-55
42-5
50-39
52-48
110-3Then glorify with the praises of your Nurturer and seek His forgiveness, truly He is oft returningفَسَبِّحْ بِحَمْدِ رَبِّكَ وَاسْتَغْفِرْهُ إِنَّهُ كَانَ تَوَّابًا