Labeling, Covering and Decomposing of Graphs — Smarandache's Notion in Graph Theory

This paper surveys the applications of Smarandache’s notion to graph theory appeared in International J.Math.Combin. from Vol.1,2008 to Vol.3,2009. In fact, many problems discussed in these papers are generalized in this paper

Induced label graphoidal graphs

Abstract. Let G be a non-trivial, simple, finite, connected and undirected graph of order n and size m

On a graph isomorphic to its intersection graph: self-graphoidal graphs

A graph G is called a graphoidal graph if there exists a graph H and a graphoidal cover ψ of H such that G ≅ Ω (H, ψ ). Then the graph G is said to be self-graphoidal if it is isomorphic to one of its graphoidal graphs. In this paper, we have examined the existence of a few self-graphoidal graphs from path length sequence of a graphoidal cover and obtained new results on self-graphoidal graphs

International Journal of Mathematical Combinatorics, Vol.3

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

AUTOMORPHISM GROUPS OF MAPS, SURFACES AND SMARANDACHE GEOMETRIES

Automorphism groups survey similarities on mathematical systems, which appear nearly in all mathematical branches, such as those of algebra, combinatorics, geometry, · · · and theoretical physics, theoretical chemistry, etc.. In geometry, configurations with high symmetry born symmetrical patterns, a kind of beautiful pictures in aesthetics. Naturally, automorphism groups enable one to distinguish systems by similarity. More automorphisms simply more symmetries of that system. This fact has established the fundamental role of automorphism groups in modern sciences. So it is important for graduate students knowing automorphism groups with applications