Antimagic Labelings of Join Graphs

被引：11

作者：

Bača M. ^{[1
]}

Phanalasy O. ^{[2
,3
]}

Ryan J. ^{[4
]}

Semaničová-Feňovčíková A. ^{[1
]}

机构：

[1] Department of Applied Mathematics and Informatics, Technical University, Košice

[2] School of Mathematical and Physical Sciences, University of Newcastle, Newcastle

[3] Department of Mathematics, National University of Laos, Vientiane

[4] School of Electrical Engineering and Computer Science, University of Newcastle, Newcastle

来源：

Mathematics in Computer Science | 2015年 / 9卷 / 2期

关键词：

Antimagic labeling; Complete multipartite graph; Join graph;

D O I：

10.1007/s11786-015-0218-0

中图分类号：

学科分类号：

摘要：

An antimagic labeling of a graph with q edges is a bijection from the set of edges of the graph to the set of positive integers $${{1, 2,dots,q}}$${1,2,⋯,q} such that all vertex weights are pairwise distinct, where a vertex weight is the sum of labels of all edges incident with the vertex. The join graph G + H of the graphs G and H is the graph with V(G+H)=V(G)∪V(H) and E(G+H)=E(G)∪E(H)∪{uv:u∈V(G)andv∈V(H)}. The complete bipartite graph Km,n is an example of join graphs and we give an antimagic labeling for Km,n,n ≥ 2m+1. In this paper we also provide constructions of antimagic labelings of some complete multipartite graphs. © 2015, Springer Basel.

引用

页码：139 / 143

页数：4

共 11 条

[1]

Alon N., Kaplan G., Lev A., Roditty Y., Yuster R., Dense graphs are antimagic, J. Graph Theory, 47, 4, pp. 297-309, (2004)

[2]

Baca M., Miller M., Super Edge-Antimagic Graphs: A Wealth of Problems and Some Solutions, (2008)

[3]

Baca M., Miller M., Phanalasy O., Semanicova-Fenovcikova A., Constructions of antimagic labelings for some families of regular graphs, J. Algorithms Comput., 44, (2013)

[4]

Cheng Y., A new class of antimagic Cartesian product graphs, Discrete Math., 308, 24, pp. 6441-6448, (2008)

[5]

Cranston D.W., Regular bipartite graphs are antimagic, J. Graph Theory, 60, 3, pp. 173-182, (2009)

[6]

Gallian J.A., A dynamic survey of graph labeling, Electron. J. Combin, 17, $${sharp}$$♯ DS6, (2014)

[7]

Hartsfield N., Ringel G., Pearls in Graph Theory: A Comprehensive Introduction, (1990)

[8]

Phanalasy O., Miller M., Rylands L.J., Lieby P., On a relationship between completely separating systems and antimagic labeling of regular graphs, LNCS, 6460, pp. 238-241, (2011)

[9]

Rylands L., Phanalasy O., Ryan J., Miller M., An application of completely separating systems to graph labeling, LNCS, 8288, pp. 376-387, (2013)

[10]

Wang T.M., Hsiao C.C., On anti-magic labeling for graph products, Discrete Math., 308, 16, pp. 3624-3633, (2008)

← 1 2 →