A graph G of order p and size q is called (a,d)-edge-antimagic total if there exists a one-to-one and onto mapping f from ∪ , ,... , such that the edge weights , ∈ form an AP progression with first term ’a’ and common difference ’d’. The graph G is said to be Super (a,d)-edge-antimagic total labeling if the , , ... , . In this paper we obtain Super (a,d)-edge-antimagic properties of certain cla...

In this paper, we consider special class of trees called uniform k-distant trees, which have many interesting properties. We show that they have an edge-magic total labeling, a super edge-magic total labeling, a (a, d)-edge-antimagic vertex labeling, an (a, d)-edgeantimagic total labeling, a super (a, d)edge-antimagic total labeling. Also we introduce a new labeling called edge bi-magic vertex ...

Restricted edge connectivity is a more refined network reliability index than edge connectivity. A restricted edge cut F of a connected graph G is an edge cut such that G−F has no isolated vertex. The restricted edge connectivity λ′ is theminimumcardinality over all restricted edge cuts.WecallG λ′-optimal if λ′ = ξ , where ξ is theminimum edgedegree inG. Moreover, a λ′-optimal graphG is called ...

Mycielski introduced a new graph transformation μ(G) for graph G, which is called the Mycielskian of G. A graph G is super connected or simply super-κ (resp. super edge connected or super-λ), if every minimum vertex cut (resp. minimum edge cut) isolates a vertex of G. In this paper, we show that for a connected graph G with |V (G)| ≥ 2, μ(G) is super-κ if and only if δ(G) < 2κ(G), and μ(G) is s...

ON SUPER EDGE-MAGIC TOTAL LABELING OF REFLEXIVE W-TREES Muhammad Imran, Mehar Ali Malik, M. Yasir Hayat Malik Department of Mathematics, School of Natural Sciences (SNS), National University of Sciences and Technology (NUST), Islamabad, Pakistan. E-mail: {imrandhab, alies.camp, yasirmalikawan}@gmail.com Mathematics Subject Classification: 05C78 ABSTRACT. Kotzig and Rosa [17] defined a magic lab...

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...

In this paper, a complete characterization of the (super) edge-magic linear forests with two components is provided. In the process of establishing this characterization, the super edge-magic, harmonious, sequential and felicitous properties of certain 2-regular graphs are investigated , and several results on super edge-magic and felicitous labelings of unions of cycles and paths are presented...