期刊名称：International Journal of Innovative Research in Science, Engineering and Technology
印刷版ISSN：2347-6710
电子版ISSN：2319-8753
出版年度：2015
卷号：4
期号：2
页码：511
DOI：10.15680/IJIRSET.2015.0402044
出版社：S&S Publications
摘要：A 𝑝. 𝑞 graph G = 𝑉, 𝐸 is said to be a square graceful graph ifthere exists an injective function f:V 𝐺 → 0,1,2,3, … , 𝑞2 such that the induced mapping 𝑓𝑝 : E 𝐺 → 1,4,9, … , 𝑞2 defined by 𝑓𝑝 𝑢𝑣 = 𝑓 𝑢 − 𝑓 𝑣is an injection. The function f is called a square graceful labeling of G. In this paper the square graceful labeling of thecaterpillar S 𝑋1, 𝑋2, … , 𝑋𝑛 , the graphs 𝑃𝑛 −1 1,2, … 𝑛 ,m𝐾1,𝑛 ∪ 𝑠𝐾1,𝑡 , 𝐾1,𝑖 , 𝑛𝑖=1 𝑃𝑛 ⨀𝐾1 − 𝑒,H graph and some othergraphsare studied. A new parameter called star square graceful deficiency number of a graph is defined and the starsquare graceful deficiency number of the cycle 𝐶3 is determined. Two new definitions namely, odd square gracefullabeling and even square graceful labeling of a graph are defined with example.
关键词：Square graceful graph; odd square graceful graph; even square graceful graph; Star square graceful;deficiency number of a graph
