Numbers, its inception, development and operations on it
Number is the language of science and the best way to express it is symbols, and numerals are forms(symbols) written by the numbers codes. Alsumariun expressed Semites for numbers letters alphabet, and the Babylonians expressed them in cuneiform, and Egyptians wrote numbers in the form of horizontal and vertical lines and fees hieroglyphics and the Greeks used first letters of words to denote numbers, as did the Phoenicians and Hebrews, while Romans used vertical lines and then evolved to take the form of letters of the alphabet. Arabs before Islam expressed numbers in terms of Alphabet and after the advent of Islam and the descent of the Holy Quran and the receipt of a lot of numbers in it written in Arabic language Muslims expressed numbers writing method instead of symbols.

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Fast parallel DNA algorithm based on adleman-lipton model: the independent dominating set problem
The independent dominating set problem is a classical optimization problem and has been shown to be NP-Complete. This study finds a molecular computing model to solve the independent dominating set problem, based on Adleman-Lipton model. It proves how to apply stickers in the sticker based model to construct the DNA solution space of the independent dominating set problem and how to apply DNA operations in the Adleman-Lipton model to solve that problem from the solution space of stickers. The time complexity of the proposed computational model is O(n + 2m) and to verify this model, a small independent dominating set problem was solved. This proves the capacity of molecular computing for solving the complex independent dominating set problem.

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Total Dominating Color Transversal number of Some familiar Graphs
A Total Dominating Color Transversal Set of a Graph G is a Total Dominating Set which is also Transversal of Some ? - Partition of vertices of G. Here ? is the Chromatic number of the graph G. Total Dominating Color Transversal number of a graph is the cardinality of a Total Dominating Color Transversal Set which has minimum cardinality among all such sets that the graph admits. In this paper we find this number for Generalized Wheel Graph, Petersen Graph, Herschel Graph, Grotszch graph and Helm Graph.

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Separation Cordial Labeling for some Star and Bistar Related Graphs
A separation cordial labeling of graph is a bijection f from to such that each edge uv is assigned the label 1 if ) is an odd number and label 0 if is an even number. Then the number of edges labeled 0 and the number of edges labeled 1 differ by at most 1. A graph has a separation cordial labeling, then it is called separation cordial graph. Here, the bistar the splitting graphs of and , the shadow graph of and square graph of are discussed and found to be separation cordial.

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Characterization of 3 – Branched Starlike Spanning Tree of a Given Two Dimensional Mesh m(m, n)
A tree T is called starlike [2], if it contains a vertex v for which deg (v) ? 3 and all other vertices of T have degree 1 or 2. If deg (v) = k, the starlike tree T is k – branched and T – v has k components, each of which are trees. In this paper, we characterize the 3 – branched starlike spanning trees of a given two dimensional mesh M(m, n) m, n ? 3 and then find its number with junction vertex [2] of degree 3.

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One Point Determining and Two Point Distinguishing Graphs
A point determining graph is defined to be a graph in which distinct non adjacent points have distinct neighborhoods. If in addition any two distinct points have distinct closed neighborhoods, it is called point distinguishing graph. A graph G is said to be one point determining, if for any two distinct vertices v_1 and v_2 ?N(v?_1)and? N(v?_2) have at most one vertex in common. A graph G is said to be two point distinguishing if for any two distinct vertices v_1 and? v?_2, the closed neighborhood ? N[v?_1] and ? N[v?_2] , have at most two vertices in common. Here we focus on some properties of one point determining and two point distinguish- ing graphs.

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Theorem on n-triangular form of fuzzy context free grammar
Every fuzzy context free language L(G) can be generated by N-triangular form of fuzzy context free grammar is Proved in this paper with illustrated examples.

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Complement of the Boolean function Graph B(Kp, INC,?Kq) of a graph
For any graph G, let V(G) and E(G) denote the vertex set and edge set of G respectively. The Boolean function graph B(Kp, INC,?Kq) of G is a graph with vertex set V(G)?E(G) and two vertices in B(Kp, INC,?Kq) are adjacent if and only if they correspond to two adjacent vertices of G, two nonadjacent vertices of G or to a vertex and an edge incident to it in G, For brevity, this graph is denoted by?B4(G). In this paper, structural properties of the complement?B4(G) of B4(G) including eccentricity properties are studied. Also, domination number and neighborhood number are found.

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Edge LICT Domination in Graphs
For any graph , the lict graph of a graph is the graph whose vertex set is the union of the set of edges and set of cut vertices of in which two vertices are adjacent if and only if corresponding members are adjacent or incident .A set of edges in a graph is called edge dominating set of if every edge in is adjacent to atleast one edge in ,denoted as and is the minimum cardinality of edge dominating set in . In this paper, many bounds on were obtained in terms of vertices , edges and other different parameters of but not in terms of elements of . Further we develop its relation with other different domination parameters.

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Total edge domination in graphs
In this paper we discuss the concept of total edge domination in graphs. We prove that for any connected (p,q) – graph G with ? < q - 1, t q - ? where ? denotes the maximum degree of an edge in G and characterize trees and unicyclic graphs which attain this bound. We also prove that t (S(G)) for any connected graph G. We also determine the value of total edge domatic number for some families of graphs.

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