Strongly multiplicative labeling of certain tree derived networks

M. Joice Punitha; A. Josephine Lissie

doi:10.26637/MJM0704/0030

Abstract

A graph $G=(V(G), E(G))$ with $p$ vertices is said to be strongly multiplicative if the vertices of $G$ can be labeled with $p$ distinct integers $1,2, \ldots, p$ such that the labels induced on the edges by the product of labels of the end vertices are all distinct [3]. In this paper we prove that the $X$ - tree, Hypertree and shuffle Hypertree are strongly multiplicative for all $n \geq 2$.

Keywords:

Hypertree, Shuffle Hypertree, Strongly multiplicative labeling, $X$-tree

Mathematics Subject Classification:

Mathematics

Authors Imprint References Funding Related Articles Downloads

M. Joice Punitha Department of Mathematics, Bharathi Women’s College, Chennai-600108, Tamil Nadu, India.
A. Josephine Lissie Department of Mathematics, Stella Maris College, Chennai-600086, Tamil Nadu, India.

Pages: 818-822
Date Published: 01-10-2019
Vol. 7 No. 04 (2019): Malaya Journal of Matematik (MJM)

B. D. Acharya, K. A. Germina and V. Ajitha, Multiplicatively Indexable Graphs in Labeling Discrete Structures and Applications, Narosa Publishing House, New Delhi, pp. $29-40,2008$.

L. W. Beineke and S. M. Hegde, Strong Multiplicative Graphs, Discuss. Math Graph Theory, 21(2001), 63-75.

G. S. Bloom and S. W. Golomb, Applications of Numbered Undirected Graphs, Proceeding of IEEE, 165(4)(1977), 562-570.

Chun-Nan Hung, Lih-Hsing Hsu, Ting-Yi Sung, Christmas Tree, A versatile 1 -fault tolerant design for token rings, Information Processing Letters, 72(1999), 55-63.

J. A. Gallian, A Dynamic Survey of Graph Labeling, Electronic Journal of Combinatorics, 2015.

K. K. Kanani and T. M. Chhaya, Strongly Multiplicative Labeling of some path related graphs, International Journal of Mathematics and Computer Applications Research, $5(5)(2015), 1-4$.

M. A. Seoud and A. Zid, Strong multiplicativity of unions and corona of paths and complete graphs, Proc. Math. Phys. Soc. Egypt, 74(1999), 59-71.

D.Paul, Indra Rajasingh, B.Sundara Rajan, Acyclic edge colouring of Hypertreeand Shuffle Hypertree, In ternational Journal of Pure and Applied Mathematics, $2(101)(2015), 623-629$.