Odd and even repetition sequences of independent domination number
Leomarich Fortugaliza Casinillo ยท Notes on Number Theory and Discrete Mathematics ยท 2020
Let {๐ ๐ } ๐=1 โ be a sequence of paths.The odd repetition sequence denoted by {๐ ๐ ๐ : ๐ โ โ} is a sequence of natural numbers in which odd numbers are repeated once and defined by {๐ ๐ ๐ } = {1, 1, 2, 3, 3, 4, 5, 5, โฆ } = {๐(๐ ๐ )} where ๐ = 2๐ -1.The even repetition sequence denoted by {๐ ๐ ๐ : ๐ โ โ} is a sequence of natural numbers, in which even numbers are repeated once and defined by {๐ ๐ ๐ } = {1, 2, 2, 3, 4, 4, 5, 6, 6, โฆ } = {๐(๐ ๐ )}, where ๐ = 2๐.In this paper, the explicit formula that shows the values of the element of two sequences {๐ ๐ ๐ } and {๐ ๐ ๐ } that depends on the subscript ๐ were constructed.Also, the formula that relates the partial sum of the elements of the said sequences, which depends on the subscript ๐ and order of the sequence of paths, were established.Further, the independent domination number of the triangular grid graph ๐ ๐ = (๐ (๐ ๐ ), ๐ธ(๐ ๐ )) will be determined using the said sequences and the two sequences will be evaluated in relation to the Fibonacci sequence {๐น ๐ } along with the order of the path.