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A graph is a useful medium for modeling of relevant parts of reality in computer science. In real life, the problem may be infinite dimensions, Design of ingenious information structure for minimizing complexity and redundancy of the problem space are versatile. Given an arbitrary 'n' node graph the problem may be infinite and in some cases it is uncountable infinite. we are limited to finite. And the problem are represented and manipulated in digital computer are also treated in the same token. The question was coding of graphs to represent in a convenient and useful way to the computer. Coding hare like graphic Integer Sequence. It is our try to show that graph theory can be viewed as a unified theory of all combinatorial structure. Any problem which is combinatorial in nature can be solved in terms of graphical structure. A good algorithm for any combinatorial problems can have costly payoff has lead to terrific advances in the state of the art. So our approaches are to make or present simple graph algorithms here. Which when stated in complex way become complex. Some problems are intractable due to lack of improvement of data structure as major criteria.