Graph theory is an important branch of applied mathematics with a lot of applications in many fields. Graph theory has a broad scale of applications in many practical situations. Graph coloring is one decent approach which can deal with many problems of graph theory. The main aim of this paper is to present the importance of graph coloring ideas in various fields for researchers that the concept of graph theory can be used by them. In this paper an overview is presented especially to project the idea of graph theory and applications of graph colouring.
In this paper, we present the sum of s+1 consecutive member of Bivariate Fibonacci Polynomials and Bivariate Lucas Polynomials and related identities consisting even and odd terms. We present its two cross two matrix and find interesting properties such as nth power of the matrix. Also, we present the identity which generalizes Catlan’s, Cassini’s and d’Ocagne’s identity. Binet’s formula will employ to obtain the identities.
This article shows the study about the harmonious coloring and to investigate the harmonious chromatic number of the central graph of quadrilateral snake, double quadrilateral snake, triple quadrilateral snake, k-quadrilateral snake, alternate quadrilateral snake, double alternate quadrilateral snake, triple alternate quadrilateral snake and k-alternate quadrilateral snake, denoted by C(Qn), C(DQn), C(TQn), C(kQn), C(AQn), C(D(AQn)), C(T(AQn)), C(k(AQn)) respectively.
Graph coloring is an important area of mathematics and computer science. Graph coloring problem is getting more famous to solve the variety of real-world problems like map coloring, timetabling and scheduling. Graph coloring is allied with two types of coloring as vertex and edge coloring. Algorithm is a set of rules that must be followed when solving a particular coloring problem and algorithms plays an important role in graph coloring. The main objective of this paper is to study of various algorithms in graph coloring.
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