New Mean Graphs

A graph that admits a Smarandachely super mean m-labeling is called a Smarandachely super m-mean graph, particularly, a mean graph if m = 2. In this paper, some new families of mean graphs are investigated. We prove that the graph obtained by two new operations called mutual duplication of a pair of vertices each from each copy of cycle Cn as well as mutual duplication of a pair of edges each from each copy of cycle Cn admits mean labeling

New results on odd harmonious labeling of graphs

Let G = (V, E) be a graph with p vertices and q edges. A graph G is said to be odd harmonious if there exists an injection f : V (G) → {0, 1, 2, · · · , 2q − 1}such that the induced function f* : E(G) → {1, 3, · · · , 2q − 1} defined by f* (uv) = f(u) + f(v) is a bijection. If f(V (G)) = {0, 1, 2, · · · , q} then f is called strongly odd harmonious labeling and the graph is called strongly odd harmonious graph. In this paper we prove that Spl(Cbn) and Spl(B(m)(n)), slanting ladder SLn, mGn, H-super subdivision of path Pn and cycle Cn, n ≡ 0(mod 4) admit odd harmonious labeling. In addition we observe that all strongly odd harmonious graphs admit mean labeling, odd mean labeling, odd sequential labeling and all odd sequential graphs are odd harmonious and all odd harmonious graphs are even sequential harmonious.Emerging Sources Citation Index (ESCI)MathScinetScopu

Perfect (super) Edge-Magic Crowns

A graph G is called edge-magic if there is a bijective function f from the set of vertices and edges to the set {1,2,…,|V(G)|+|E(G)|} such that the sum f(x)+f(xy)+f(y) for any xy in E(G) is constant. Such a function is called an edge-magic labelling of G and the constant is called the valence. An edge-magic labelling with the extra property that f(V(G))={1,2,…,|V(G)|} is called super edge-magic. A graph is called perfect (super) edge-magic if all theoretical (super) edge-magic valences are possible. In this paper we continue the study of the valences for (super) edge-magic labelings of crowns Cm¿K¯¯¯¯¯n and we prove that the crowns are perfect (super) edge-magic when m=pq where p and q are different odd primes. We also provide a lower bound for the number of different valences of Cm¿K¯¯¯¯¯n, in terms of the prime factors of m.Postprint (updated version