**4. Conclusion**

**Proof.** If *G*<sup>1</sup> and *G*<sup>2</sup> are chaotic connected and not chaotic cores graphs, then we

i. A polymer is composed of many repeating units called monomers. Starch, cellulose, and proteins are natural polymers. Nylon and polyethylene are synthetic polymers. Polymerization is the process of joining monomers. Polymers may be formed by addition polymerization; furthermore, one essential advance likewise polymerization is mix as in **Figure 4**, which happens when the polymer's development is halted by free electrons from two developing chains that join and frame a solitary chain. The accompanying chart portrays mix, with the image (R) speaking to whatever remains of the

ii. Chemical nature of enzymes, all known catalysts are proteins. They are high atomic weight mixes made up primarily of chains of amino acids connected

, and each of them are isomorphic to *k*2. Since *k*<sup>2</sup> ≈*k*<sup>2</sup> ⊻ *k*<sup>2</sup> it follows

<sup>⊻</sup> lim*n*!<sup>∞</sup> *<sup>f</sup> <sup>n</sup> <sup>G</sup>*<sup>2</sup>

*,* lim*n*!<sup>∞</sup> *<sup>f</sup> <sup>n</sup> <sup>G</sup>*<sup>1</sup>

*:*

and

∗ *π*<sup>1</sup> lim*n*!<sup>∞</sup> *f <sup>n</sup> G*<sup>2</sup>  *,*

get the following chaotic induced graphs lim*n*!<sup>∞</sup> *f <sup>n</sup> G*<sup>1</sup> ⊻ *G*<sup>2</sup>

= *π*<sup>1</sup> lim*n*!<sup>∞</sup> *f <sup>n</sup> G*<sup>1</sup> 

<sup>¼</sup> lim*n*!<sup>∞</sup> *<sup>f</sup> <sup>n</sup> <sup>G</sup>*<sup>1</sup>

together by peptide bonds as in **Figure 5**.

lim*n*!<sup>∞</sup> *f <sup>n</sup> G*<sup>2</sup>

*Functional Calculus*

that lim*n*!<sup>∞</sup> *f <sup>n</sup> G*<sup>1</sup> ⊻ *G*<sup>2</sup>

*π*<sup>1</sup> lim*n*!<sup>∞</sup> *f <sup>n</sup> G*<sup>1</sup> ⊻ *G*<sup>2</sup> 

**3. Some applications**

chain.

**Figure 4.** *Polymerization.*

**Figure 5.**

**56**

*Typical amino acids.*

In this chapter, the fundamental group of the limit chaotic foldings on chaotic connected edge graphs is deduced. Also, we can deduce some algorithms from a new operation of a graph by using the adjacency matrices.
