# On super d-face antimagic total labelings of the corona product of a tree with r copies of a path

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An edge-colored graph G is rainbow connected, if any two vertices are connected by a path whose edges have distinct colors. The rainbow connection number of a connected graph G, denoted rc(G), is the smallest number of colors that are needed in order to make G rainbow connected. In this paper we...

- Characterizing all graphs containing cycles with locating-chromatic number 3. Asmiati; Baskoro, Edy Tri // AIP Conference Proceedings;5/22/2012, Vol. 1450 Issue 1, p351
Let G be a connected graph G. Let c be a k-coloring of V(G) which induces an ordered partition Î = {S1,S2, ...,Sk} of V(G), where Si is the set of vertices receiving color i. The color code cÎ (Î½) of vertex Î½ is the ordered k-tuple (d(Î½,S1), d(Î½, S2), ..., d(Î½, Sk)), where...

- 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...

- ACYCLIC 6-COLOURING OF GRAPHS WITH MAXIMUM DEGREE 5 AND SMALL MAXIMUM AVERAGE DEGREE. FIEDOROWICZ, ANNA // Discussiones Mathematicae: Graph Theory;2013, Vol. 33 Issue 1, p91
A k-colouring of a graph G is a mapping c from the set of vertices of G to the set {1, ..., k} of colours such that adjacent vertices receive distinct colours. Such a k-colouring is called acyclic, if for every two distinct colours i and j, the subgraph induced by all the edges linking a vertex...

- UPPER BOUNDS ON THE b-CHROMATIC NUMBER AND RESULTS FOR RESTRICTED GRAPH CLASSES. ALKHATEEB, MAIS; KOHL, ANJA // Discussiones Mathematicae: Graph Theory;2011, Vol. 31 Issue 4, p709
A b-coloring of a graph G by Îº colors is a proper vertex coloring such that every color class contains a color-dominating vertex, that is, a vertex having neighbors in all other Îº-1 color classes. The b-chromatic number Î§b(G) is the maximum integer Îº for which G has a b-coloring by k...

- Î³-LABELINGS OF COMPLETE BIPARTITE GRAPHS. Bullington, Grady D.; Eroh, Linda L.; Winters, Steven J. // Discussiones Mathematicae: Graph Theory;2010, Vol. 30 Issue 1, p45
Explicit formulae for the Î³-min and Î³-max labeling values of complete bipartite graphs are given, along with Î³-labelings which achieve these extremes. A recursive formula for the Î³-min labeling value of any complete multipartite is also presented.

- Further Results on Product Cordial Labeling. Vaidya, S. K.; Barasara, C. M. // International Journal of Mathematical Combinatorics;Jul2012, Vol. 3, p64
We prove that closed helm CHn, web graph Wbn, flower graph Fln, double triangular snake DTn and gear graph Gn admit product cordial labeling.

- Odd Harmonious Labeling of Some Graphs. Vaidya, S. K.; Shah, N. H. // International Journal of Mathematical Combinatorics;Jul2012, Vol. 3, p105
The labeling of discrete structures is a potential area of research due to its wide range of applications. The present work is focused on one such labeling called odd harmonious labeling. A graph G is said to be odd harmonious if there exist an injection Æ’ : V (G) â†’ {0, 1, 2, . . . ,...

- Super (a,d)-Fn - Antimagic Total Labeling for a Connected and Disconnected Amalgamation of Fan Graphs. Dafik; Ika Hesti Agustin; Khuri Faridatun N. // AIP Conference Proceedings;2016, Vol. 1707 Issue 1, p1
All graph in this paper are finite, simple and undirected. Let G = (V(G),E(G)) be a graph of order p and size q. Graph G admits a H-covering, if every edge in E(G) belongs to at least one subgraph of G isomorphic to a given graph H. A graph G is said to be an (a,d)-H-antimagic total labeling if...