On the Structure of Graphs with Non-Surjective L(2, 1)-Labelings

Path covering number and L(2,1)-labeling number of graphs

A path covering of a graph G is a set of vertex disjoint paths of G containing all the vertices of G. The path covering number of G, denoted by P (G), is the minimum number of paths in a path covering of G. An k-L(2, 1)-labeling of a graph G is a mapping f from V (G) to the set {0, 1, . . . , k} such that |f(u) − f(v)| ≥ 2 if dG(u, v) = 1 and |f(u) − f(v)| ≥ 1 if dG(u, v) = 2. The L(2, 1)-label...

Construction of Large Graphs with No Optimal Surjective L(2, 1)-Labelings

Balanced Degree-Magic Labelings of Complete Bipartite Graphs under Binary Operations

A graph is called supermagic if there is a labeling of edges where the edges are labeled with consecutive distinct positive integers such that the sum of the labels of all edges incident with any vertex is constant. A graph G is called degree-magic if there is a labeling of the edges by integers 1, 2, ..., |E(G)| such that the sum of the labels of the edges incident with any vertex v is equal t...

Graceful labelings of the generalized Petersen graphs

A graceful labeling of a graph $G=(V,E)$ with $m$ edges is aninjection $f: V(G) rightarrow {0,1,ldots,m}$ such that the resulting edge labelsobtained by $|f(u)-f(v)|$ on every edge $uv$ are pairwise distinct. For natural numbers $n$ and $k$, where $n > 2k$, a generalized Petersengraph $P(n, k)$ is the graph whose vertex set is ${u_1, u_2, cdots, u_n} cup {v_1, v_2, cdots, v_n}$ and its edge set...

Constructions of antimagic labelings for some families of regular graphs

In this paper we construct antimagic labelings of the regular complete multipartite graphs and we also extend the construction to some families of regular graphs.