Recently, Braunstein et al. [1] introduced normalized Laplacian matrices of graphs as density matrices in quantum mechanics and studied the relationships between quantum physical properties and graph theoretical properties of the underlying graphs. We provide further results on the multipartite separability of Laplacian matrices of graphs. In particular, we identify complete bipartite graphs wh...

Recently three prime cordial labeling behavior of path, cycle, complete graph, wheel, comb, subdivison of a star, bistar, double comb, corona of tree with a vertex, crown, olive tree and other standard graphs were studied. Also four prime cordial labeling behavior of complete graph, book, flower were studied. In this paper, we investigate the four prime cordial labeling behavior of corona of wh...

Let G = (V,E) be a finite (non-empty) graph, where V and E are the sets of vertices and edges of G. An edge magic total labeling is a bijection α from V ∪E to the integers 1,2, . . . , n+e, with the property that for every xy ∈E, α(x)+α(y)+α(xy)= k, for some constant k. Such a labeling is called an a-vertex consecutive edge magic total labeling if α(V )= {a + 1, . . . , a + n} and a b-edge cons...

The L(2, 1)-labeling of a digraph G is a function f from the node set of G to the set of all nonnegative integers such that |f(x) − f(y)| ≥ 2 if x and y are at distance 1, and f(x) 6= f(y) if x and y are at distance 2, where the distance from vertex x to vertex y is the length of a shortest dipath from x to y. The minimum of the maximum used label over all L(2, 1)-labelings of G is called λ(G)....

The concept of -labeling in graph come into existence with the solution of frequency assignment problem. In fact, in this problem a frequency in the form of nonnegative integers is to assign to each radio or TV transmitters located at various places such that communication does not interfere. This frequency assignment problem can be modeled with vertex labeling of graphs. An -labeling (or dista...

A digraph D with p vertices and q arcs is labeled by assigning a distinct integer value g(v) from {0, 1, ..., q} to each vertex v. The vertex values, in turn, induce a value g(u, v) on each arc (u, v) where g(u, v) = (g(v)− g(u))(mod q + 1). If the arc values are all distinct then the labeling is called a graceful labeling of a digraph. In this paper, we prove a general result on graceful digra...

In this paper, we are studying vertex-magic total labelings of simple graphs. We introduce a procedure called mutation which transforms one labeling into another by swapping sets of edges among vertices. The result of a mutation may be a different labeling of the same graph or a labeling of a different graph. Mutation proves to be a remarkably fruitful process— for example we are able to genera...

We define a total k-labeling φ of graph G as combination an edge labeling φe:E(G)→{1,2,…,ke} and vertex φv:V(G)→{0,2,…,2kv}, such that φ(x)=φv(x) if x∈V(G) φ(x)=φe(x) x∈E(G), where k= max {ke,2kv}. The is called irregular reflexive every two different edges has distinct weights, the weight defined summation label itself its labels. Thus, smallest value k for which strength G. In this paper, we ...

Consider a graph G with |V (G)| = p and |E(G)| q let f : V (G) → {k, k + 1, 2, . − 1}} be an injective function. The induced edge labeling ∗ for vertex is defined by (e) all e uv ∈ E(G) bijective. If f(V (G)) ∪ {f E(G)} , 1}, then called k-super cube root mean labeling. such exists, graph. In this paper, I introduce prove the existence of to graphs viz., triangular snake Tn, double D(Tn), Quadr...

A graph G admits an H-covering if every edge of belongs to a subgraph isomorphic given H. is said be H-magic there exists bijection f:V(G)∪E(G)→{1,2,…,|V(G)|+|E(G)|} such that wf(H′)=∑v∈V(H′)f(v)+∑e∈E(H′)f(e) constant, for H′ In particular, H-supermagic f(V(G))={1,2,…,|V(G)|}. When H complete K2, H-(super)magic labeling edge-(super)magic labeling. Suppose F-covering and two graphs F We define (...