Graph labeling is considered as one of the most interesting areas in graph theory. A for a simple G (numbering or valuation), an association non -negative integers to vertices G  (vertex labeling) edges (edge both them. In this paper we study graceful k- uniform hypertree and define condition corresponding tree be graceful. if minimum difference vertices’ labels each edge dis...

Gallai proved that the vertex set of any graph can be partitioned into two sets, each inducing a subgraph with all degrees even. We prove that every connected graph of even order has a vertex partition into sets inducing subgraphs with all degrees odd, and give bounds for the number of sets of this type required for vertex partitions and vertex covers. We also give results on the partitioning a...

A vertex irregular total k-labeling of a graph G with vertex set V and edge set E is an assignment of positive integer labels {1, 2, ..., k} to both vertices and edges so that the weights calculated at vertices are distinct. The total vertex irregularity strength of G, denoted by tvs(G)is the minimum value of the largest label k over all such irregular assignment. In this paper, we study the to...

Surface roughness, often captured through root-mean-square roughness (Rrms), has been shown to impact the quality of self-assembled monolayers (SAMs) formed on coinage metals. Understanding the effect of roughness on hydrophobicity of SAMs, however, is complicated by the odd-even effect-a zigzag oscillation in contact angles with changes in molecular length. We recently showed that for surfaces...

The NP-complete problem Feedback Vertex Set is that of deciding whether or not it is possible, for a given integer k ≥ 0, to delete at most k vertices from a given graph so that what remains is a forest. The variant in which the deleted vertices must form an independent set is called Independent Feedback Vertex Set and is also NP-complete. In fact, even deciding if an independent feedback verte...

Let G be a graph and f : V (G) → {1, 2, 3, . . . , p+ q} be an injection. For each edge e = uv and an integer m ≥ 2, the induced Smarandachely edge m-labeling f∗ S is defined by f ∗ S(e) = ⌈ f(u) + f(v) m ⌉ . Then f is called a Smarandachely super m-mean labeling if f(V (G))∪ {f∗(e) : e ∈ E(G)} = {1, 2, 3, . . . , p+ q}. Particularly, in the case of m = 2, we know that f ∗(e) =    f(u)+f(v) ...