Let [n]∗ denote the set of integers {−n−1 2 , . . . , n−1 2 } if n is odd, and {−n 2 , . . . , n 2 } \ {0} if n is even. A super edge-graceful labeling f of a graph G of order p and size q is a bijection f : E(G) → [q]∗, such that the induced vertex labeling f ∗ given by f ∗(u) = ∑ uv E(G) f(uv) is a bijection f ∗ : V (G) → [p]∗. A graph is super edge-graceful if it has a super edge-graceful la...

Let G be a subdivision of a ladder graph. In this paper we study magic evaluation with type (1, 1, 1) for a given any general ladder graph G. We prove that subdivided ladder admits magic evaluation having type (1, 1, 1). We also prove such a subdivision admits consecutive magic evaluation having type (1, 1, 0). AMS (MOS) Subject Classification Codes: 05C78

Let G be a connected graph that is the edge-disjoint union of two paths of length n, where n ≥ 2. Using a result of Thomason on decompositions of 4-regular graphs into pairs of Hamiltonian cycles, we prove that G has a third path of length n. The “two-path conjecture” states that if a graph G is the edge-disjoint union of two paths of length n with at least one common vertex, then the graph has...

An anti-magic labeling of a finite simple undirected graph with p vertices and q edges is a bijection from the set of edges to the set of integers {1, 2, ..., q} such that the vertex sums are pairwise distinct, where the vertex sum at vertex u is the sum of labels of all edges incident to such vertex. A graph is called anti-magic if it admits an antimagic labeling. Hartsfield and Ringel conject...

A n-vertex graph is said to be decomposable if for any partition (λ1, . . . , λp) of the integer n, there exists a sequence (V1, . . . , Vp) of connected vertex-disjoint subgraphs with |Vi| = λi. The aim of the paper is to study the homeomorphism classes of decomposable trees. More precisely, we show that homeomorphism classes containing decomposable trees with an arbitrarily large minimal dist...

In the present paper the question is studied from three points of vieAv whether to any natural number k _> 2 there exists a complete graph decomposable into k factors with diameters two . The affirmative answer to this question is given and some estimations for the minimal possible number of vertices of such a complete graph are deduced . As a corollary it follows that given k diameters di, d2 ...

Given a graph G = (V, E), V(G) = V and E(G) = E denote the vertex set and the edge set of G, respectively. All graphs considered in this paper are undirected graphs. A simple path (or path for short) is a sequence of adjacent edges (v1, v2), (v2, v3), ..., (vm-2, vm-1), (vm-1, vm), written as 〈v1, v2, v3, ..., vm〉, in which all of the vertices v1, v2, v3, ..., vm are distinct except possibly v1...

A graph G = (V,E) is arbitrarily vertex decomposable if for any sequence τ of positive integers adding up to |V |, there is a sequence of vertex-disjoint subsets of V whose orders are given by τ , and which induce connected graphs. The main aim of this paper is to study the recursive version of this problem. We present a solution for trees, suns, and partially for a class of 2-connected graphs ...