An Algorithm for Odd Graceful Labeling of the Union of Paths and Cycles

In 1991, Gnanajothi [4] proved that the path graph P_n with n vertex and n-1 edge is odd graceful, and the cycle graph C_m with m vertex and m edges is odd graceful if and only if m even, she proved the cycle graph is not graceful if m odd. In this paper, firstly, we studied the graph C_m $\cup$ P_m when m = 4, 6,8,10 and then we proved that the graph C_ $\cup$ P_n is odd graceful if m is even. Finally, we described an algorithm to label the vertices and the edges of the vertex set V(C_m $\cup$ P_n) and the edge set E(C_m $\cup$ P_n).Comment: 9 Pages, JGraph-Hoc Journa

Some Topics of Special Interest in Graph Theory

Not availabl

Some Investigations in the Theory of Graphs

Not availabl

Discussion On Some Important Topics in Graph Theory

Not availabl

A Study on Graph Theory of Path Graphs

A simple graph G = (V, E) consists of V , a nonempty set of vertices, and E, a set of unordered pairs of distinct elements of V called edges. Simple graphs have their limits in modeling the real world. Instead, we use multigraphs, which consist of vertices and undirected edges between these vertices, with multiple edges between pairs of vertices allowed. In the mathematical field of graph theory, a path graph or linear graph is a graph whose vertices can be listed in the order v1, v2, …, vn such that the edges are {vi, vi+1} where i = 1, 2, …, n ? 1. Equivalently, a path with at least two vertices is connected and has two terminal vertices (vertices that have degree 1), while all others (if any) have degree 2. Paths are often important in their role as subgraphs of other graphs, in which case they are called paths in that graph. A path is a particularly simple example of a tree, and in fact the paths are exactly the trees in which no vertex has degree 3 or more. A disjoint union of paths is called a linear forest

International Journal of Mathematical Combinatorics, Vol.2

The International J.Mathematical Combinatorics (ISSN 1937-1055) is a fully refereed international journal, sponsored by the MADIS of Chinese Academy of Sciences and published in USA quarterly comprising 460 pages approx. per volume, which publishes original research papers and survey articles in all aspects of Smarandache multi-spaces, Smarandache geometries, mathematical combinatorics, non-euclidean geometry and topology and their applications to other sciences