### 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

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#### References

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

eISSN 0975-5748; pISSN 0974-875X 