# Vertex Graceful Labeling-Some Path Related Graphs

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- The Cycle Discrepancy of Three-Regular Graphs. Abbasi, Sarmad; Aslam, Laeeq // Graphs & Combinatorics;Jan2011, Vol. 27 Issue 1, p27
Let G = ( V, E) be an undirected graph and $${{\mathcal C}(G)}$$ denote the set of all cycles in G. We introduce a graph invariant cycle discrepancy, which we define as We show that, if G is a three-regular graph with n vertices, then This bound is best possible and is achieved by very simple...

- On Mean Graphs. Vasuki, R.; Arockiaraj, S. // International Journal of Mathematical Combinatorics;Sep2013, Vol. 3, p22
Let G(V,E) be a graph with p vertices and q edges. For every assignment f : V (G) â†’ {0, 1, 2, 3, ..., q}, an induced edge labeling f* : E(G) â†’ {1, 2, 3, ..., q} is Â… if f(u) and f(v) are of the same parity otherwise for every edge uv âˆˆ E(G). If f*(E) = {1, 2, ..., q}, then...

- On Mean Cordial Graphs. Ponraj, R.; Sivakumar, M. // International Journal of Mathematical Combinatorics;Sep2013, Vol. 3, p78
Let f be a function from the vertex set V (G) to {0, 1, 2}. For each edge uv assign the label [f(u) + f(v)/2]. f is called a mean cordial labeling if |vf(i) - vf(j)| â‰¤ 1 2 and |ef(i) - ef(j)| â‰¤ 1, i, j âˆˆ {0, 1, 2}, where vf(x) and ef(x) respectively are denote the number of...

- Solution of a Conjecture on Skolem Mean Graph of Stars K1,l Ï… K1,m Ï… K1,n. Balaji, V. // International Journal of Mathematical Combinatorics;Dec2011, Vol. 4, p115
In this paper, we prove a conjecture that the three stars K1,l Ï… K1,m Ï… K1,n is a skolem mean graph if |m - n| < 4 + l for integers l, m â‰¤ 1 and l â‰¥ m < n.

- H-magic covering on some classes of graphs. Roswitha, Mania; Baskoro, Edy Tri // AIP Conference Proceedings;5/22/2012, Vol. 1450 Issue 1, p135
For a graph G(V,E), an edge-covering of G is a family of different subgraphs H1,...Hk such that any edge of E belongs to at least one of the subgraphs Hi, 1 â‰¤ i â‰¤ k. If every Hi is isomorphic to a given graph H, then G admits an H-covering. Graph G is said to be H-magic if G has an...

- Vertex-antimagic labelings of regular graphs. Ahmad, Ali; Ali, Kashif; Bača, Martin; Kovář, Petr; Semaničová-Feňovčíková, Andrea // Acta Mathematica Sinica;Sep2012, Vol. 28 Issue 9, p1865
Let G = ( V,E) be a finite, simple and undirected graph with p vertices and q edges. An ( a, d)-vertex-antimagic total labeling of G is a bijection f from V ( G) âˆª E( G) onto the set of consecutive integers 1, 2, ..., p + q, such that the vertex-weights form an arithmetic progression with...

- Degree Splitting Graph on Graceful, Felicitous and Elegant Labeling. Selvaraju, P.; Balaganesan, P.; Renuka, J.; Balaj, V. // International Journal of Mathematical Combinatorics;Apr2012, Vol. 2, p96
We show that the degree splitting graphs of Bn,n; Pn; Km,n; n(k4 -3e)I; n(k4 - 3e)II(b); n(k4 - e)II and n(k4 - 2e)II(a) are graceful [3]. We prove C3 ï¿½K1,n is graceful, felicitous and elegant [2], Also we prove K2,n is felicitous and elegant.

- Fibonacci and Super Fibonacci Graceful Labelings of Some Cycle Related Graphs. Vaidya, S. K.; Prajapati, U. M. // International Journal of Mathematical Combinatorics;Dec2011, Vol. 4, p59
No abstract available.

- UNDERLYING GRAPHS OF 3-QUASI-TRANSITIVE DIGRAPHS AND 3-TRANSITIVE DIGRAPHS RUIXIA WANG, SHIYING WANG. RUIXIA WANG; SHIYING WANG // Discussiones Mathematicae: Graph Theory;2013, Vol. 33 Issue 2, p429
A digraph is 3-quasi-transitive (resp. 3-transitive), if for any path x0x1 x2x3 of length 3, x0 and x3 are adjacent (resp. x0 dominates x3). CÃ©sar HernÃ¡ndez-Cruz conjectured that if D is a 3-quasi-transitive digraph, then the underlying graph of D, UG(D), admits a 3-transitive orientation....