3-Total Sum Cordial Labeling on Some New Graphs

Poulomi Ghosh, Sumonta Ghosh, Anita Pal

Abstract


Let \(G=(V,E)\) be a graph with vertex set \(V\) and edge set \(E\). Consider a vertex labeling \(f:V(G)\to \{0,1,2\}\) such that each edge \(uv\) assign the label \((f(u)+f(v))\ (\{{\rm mod}\  3)\). The map \(f\) is called a 3-total sum cordial labeling if \(|f(i)-f(j)|\le 1\), for \(i,j \in \{0,1,2\}\) where \(f(x)\) denotes the total number of vertices and edges labeled with \(x=\{0,1,2\}\). Any graph which satisfied 3-total sum cordial labeling is called a 3-total sum cordial graph. Here we prove some graphs like wheel, globe and a graph obtained by switching and duplication of arbitrary vertex of a cycle are 3-total sum cordial graphs.

Keywords


3-total sum cordial labeling; 3-total sum cordial graph; Globe; Vertex switching; Vertex duplication

Full Text:

PDF

References


I. Cahit, Cordial graphs: A weaker version of graceful and harmonious graphs, Ars. Combinatorial 23 (1987), 201–207.

J.A. Gallian, A dynamic survey of graph labeling, The Electronic Journal of Combinatorics 17 (2010), DS6.

F. Harrary, Graph Theory, Narosa Publishing House (2001).

S. Pethanachi Selvam and G. Lathamaheshwari, k sum cordial labelling for some graphs, International Journal of Mathematical Archive 4 (3) (2013), 253 – 259.

J. Shiama, Sum cordial labelling for some graphs, International Journal of Mathematical Archive 3 (9) (2012), 3271 – 3276.

P. Ghosh and A. Pal, Some new Fibonacci divisor cordial graphs, Advanced Modelling and Optimization 17 (2015), 221 – 232.

A. Tenguria and R. Verma, 3-total super sum cordial labelling for some graphs, International Journal of Applied Information Systems 8 (4) (2015), 25 – 30.




DOI: http://dx.doi.org/10.26713%2Fjims.v9i3.815

eISSN 0975-5748; pISSN 0974-875X