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The theory of colorful graphs can be developed by working in Galois field modulo (p), p > 2 and a prime number. The paper proposes a program of possible conversion of graph theory into a pleasant colorful appearance. We propose to paint the usual black (indicating presence of an edge) and white (indicating absence of an edge) edges of graphs using multitude of colors and study their properties. All colorful graphs considered here are simple, i.e. not having any multiple edges or self-loops. This paper is an invitation to the program of generalizing usual graph theory in this direction.
Given an $n$ vertex graph whose edges have colored from one of $r$ colors $C={c_1,c_2,ldots,c_r}$, we define the Hamilton cycle color profile $hcp(G)$ to be the set of vectors $(m_1,m_2,ldots,m_r)in [0,n]^r$ such that there exists a Hamilton cycle th
The problem of finding paths in temporal graphs has been recently considered due to its many applications. In this paper we consider a variant of the problem that, given a vertex-colored temporal graph, asks for a path whose vertices have distinct co
Let $P(G,lambda)$ denote the number of proper vertex colorings of $G$ with $lambda$ colors. The chromatic polynomial $P(C_n,lambda)$ for the cycle graph $C_n$ is well-known as $$P(C_n,lambda) = (lambda-1)^n+(-1)^n(lambda-1)$$ for all positive integer
The concept of graceful labels was proposed by Rosa, scholars began to study graceful labels of various graphs and obtained relevant results.Let the graph is a bipartite graceful graph, we have proved some graphs are graceful labeling in this paper.
A new characterisation of Hamiltonian graphs using f-cutset matrix is proposed. A new exact polynomial time algorithm for the travelling salesman problem (TSP) based on this new characterisation is developed. We then define so called ordered weighted