In my search for the definition for the poetry term "doggerel," which I still do not understand, I came across the term "irregular rhyme." Can someone explain the definition of these terms, and how they are used in the literary sense?
Irregular rhyme usually, as @deadrat mentioned, means something which does not fit into any repetitive rhyming sequence: so a Shakesperian sonnet with line endings AAB CCB DDE FFE is regular, AAB CBC CAB BCA is not. The difference is kinda sketchy, though: is a limerick (AABBA) regular?
So in real terms, regular rhyme just means "fitting with the rule of an established rhyme pattern". If a listener can anticipate the ending of the next line, then it's regular. A good example of a subversion of this for use in doggerel is "The Assumption Song".
AN irregular rhyme, though, can sometimes mean a poem (aka 'rhyme') with perfectly regular rhyme, but with irregular meter. Once again, regular just means "what people expect". And meter is just which syllables or sets of syllables are unstressesd, and which aren't. So a limerick goes something like:
da DA da DA da DA da da DA da DA da DA da da DA da DA da DA da DA da DA da DA da DA da
(where the unstressed 'da's can be multiple syllables and sometimes even left off)
A wonderful bird is the pelican, His bill will hold more than his belican, He can take in his beak Enough food for a week But I'm damned if I see how the helican!
There was a young man from Japan Whose limericks never would scan. When asked why that was, He replied "It's because I always try to cram as many words into the last line as I possibly can."
[Following included because I misread the question initially as being what Doggerel is]:
Doggerel is often used by poets to describe poetry which doesn't follow the traditional rules of meter and rhyme: which, in short, is what irregular rhyme is.
In layman's conversational English, doggerel just means any poetry - especially naive or earthy poetry - which is not intended to be judged for its artistry or high-minded ideas.
Casually-written limericks, for example, while fitting perfectly to the limerick style, often get called doggerel if their main point is bawdy humor rather than artistry. The same with children's school-yard chants, nursery rhymes, etc.
It's also sometimes used self-effacingly by poets to describe their own work, in the same way as calligraphers might refer to their own work as "chicken-scratch".
Some forms of poetry have a fixed set of rules, including rules for how the last syllables of the lines of a poem rhyme. These are usually indicated by letters. For example, an Italian sonnet starts with an octave or two quatrains (four-line units), each with a pattern
That is, for each quatrain the first and fourth lines rhyme, and the second and third lines rhyme but with a different sound from the first and fourth. In contrast, in poems with an irregular rhyme, the rhyming lines do not form any discernible pattern like the above.