New Constructions of Edge Bimagic Graphs from Magic Graphs

ABSTRACT

An edge magic total labeling of a graph G(V,E) with p vertices and q edges is a bijection f from the set of vertices and edges to such that for every edge uv in E, f(u) + f(uv) + f(v) is a constant k. If there exist two constants k_{1} and k_{2} such that the above sum is either k_{1} or k_{2}, it is said to be an edge bimagic total labeling. A total edge magic (edge bimagic) graph is called a super edge magic (super edge bimagic) if f(V(G)) = . In this paper we define super edge edge-magic labeling and exhibit some interesting constructions related to Edge bimagic total labeling.

An edge magic total labeling of a graph G(V,E) with p vertices and q edges is a bijection f from the set of vertices and edges to such that for every edge uv in E, f(u) + f(uv) + f(v) is a constant k. If there exist two constants k

Cite this paper

nullJ. Babujee and B. Suresh, "New Constructions of Edge Bimagic Graphs from Magic Graphs,"*Applied Mathematics*, Vol. 2 No. 11, 2011, pp. 1393-1396. doi: 10.4236/am.2011.211197.

nullJ. Babujee and B. Suresh, "New Constructions of Edge Bimagic Graphs from Magic Graphs,"

References

[1] J. A. Gallian, “A Dynamic Survey of Graph Labeling,” Electronic Journal of Combinatorics, Vol. 17, No. 1, 2010, pp. 1-246.

[2] N. Hartsfield and G. Ringel, “Pearls in Graph Theory,” Academic Press, Cambridge, 1990.

[3] A. Kotzig and A. Rosa, “Magic Valuations of Finite Graphs,” Canadian Mathematical Bulletin, Vol. 13, 1970, pp. 451-461. doi:10.4153/CMB-1970-084-1

[4] W. D. Wallis, “Magic Graphs,” Birkhauser, Basel, 2001. doi:10.1007/978-1-4612-0123-6

[5] J. B. Babujee, “Bimagic Labeling in Path Graphs,” The Mathematics Education, Vol. 38, No. 1, 2004, pp. 12-16.

[6] J. B. Babujee, “On Edge Bimagic Labeling,” Journal of Combinatorics Information & System Sciences, Vol. 28, No. 1-4, 2004, pp. 239-244.

[7] J. B. Babujee and R. Jagadesh, “Super Edge Bimagic Labeling for Trees” International Journal of Analyzing methods of Components and Combinatorial Biology in Mathematics, Vol. 1 No. 2, 2008, pp. 107-116.

[8] J. B. Babujee and R. Jagadesh, “Super Edge Bimagiclabeling for Graph with Cycles,” Pacific-Asian Journal of Mathematics, Vol. 2, No. 1-2, 2008, pp. 113-122.

[9] J. B. Babujee and R. Jagadesh, “Super Edge Bimagic Labeling for Disconnected Graphs,” International Journal of Applied Mathematics & Engineering Sciences, Vol. 2, No. 2, 2008, pp. 171-175.

[10] J. B. Babujee and R. Jagadesh, “Super Edge Bimagic Labeling for Some Class of Connected Graphs Derived from Fundamental Graphs,” International Journal of Combinatorial Graph Theory and Applications, Vol. 1, No. 2, 2008, pp. 85-92.

[1] J. A. Gallian, “A Dynamic Survey of Graph Labeling,” Electronic Journal of Combinatorics, Vol. 17, No. 1, 2010, pp. 1-246.

[2] N. Hartsfield and G. Ringel, “Pearls in Graph Theory,” Academic Press, Cambridge, 1990.

[3] A. Kotzig and A. Rosa, “Magic Valuations of Finite Graphs,” Canadian Mathematical Bulletin, Vol. 13, 1970, pp. 451-461. doi:10.4153/CMB-1970-084-1

[4] W. D. Wallis, “Magic Graphs,” Birkhauser, Basel, 2001. doi:10.1007/978-1-4612-0123-6

[5] J. B. Babujee, “Bimagic Labeling in Path Graphs,” The Mathematics Education, Vol. 38, No. 1, 2004, pp. 12-16.

[6] J. B. Babujee, “On Edge Bimagic Labeling,” Journal of Combinatorics Information & System Sciences, Vol. 28, No. 1-4, 2004, pp. 239-244.

[7] J. B. Babujee and R. Jagadesh, “Super Edge Bimagic Labeling for Trees” International Journal of Analyzing methods of Components and Combinatorial Biology in Mathematics, Vol. 1 No. 2, 2008, pp. 107-116.

[8] J. B. Babujee and R. Jagadesh, “Super Edge Bimagiclabeling for Graph with Cycles,” Pacific-Asian Journal of Mathematics, Vol. 2, No. 1-2, 2008, pp. 113-122.

[9] J. B. Babujee and R. Jagadesh, “Super Edge Bimagic Labeling for Disconnected Graphs,” International Journal of Applied Mathematics & Engineering Sciences, Vol. 2, No. 2, 2008, pp. 171-175.

[10] J. B. Babujee and R. Jagadesh, “Super Edge Bimagic Labeling for Some Class of Connected Graphs Derived from Fundamental Graphs,” International Journal of Combinatorial Graph Theory and Applications, Vol. 1, No. 2, 2008, pp. 85-92.