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Some new results on power cordial labeling
C.M. Barasara,Y.B. Thakkar 한국전산응용수학회 2023 Journal of applied mathematics & informatics Vol.41 No.3
A power cordial labeling of a graph $G = (V(G), E(G))$ is a bijection $f: V(G) \rightarrow \lbrace 1, 2, ..., |V(G)| \rbrace$ such that an edge $e=uv$ is assigned the label $1$ if $f(u)=(f(v))^{n}$ or $f(v)=(f(u))^{n}$, For some $n\in \mathbb{N} \cup \lbrace 0 \rbrace$ and the label $0$ otherwise, then the number of edges labeled with $0$ and the number of edges labeled with $1$ differ by at most $1$. In this paper, we investigate power cordial labeling for helm graph, flower graph, gear graph, fan graph and jewel graph as well as larger graphs obtained from star and bistar using graph operations.
C.M. Barasara,Y.B. Thakkar 한국전산응용수학회 2024 Journal of applied mathematics & informatics Vol.42 No.2
A power cordial labeling of a graph $G = (V(G), E(G))$ is a bijection $f: V(G) \rightarrow \lbrace 1, 2, ..., |V(G)| \rbrace$ such that an edge $e=uv$ is assigned the label $1$ if $f(u)=(f(v))^{n}$ or $f(v)=(f(u))^{n}$, for some $n\in \mathbb{N} \cup \lbrace 0 \rbrace$ and the label $0$ otherwise, then the number of edges labeled with $0$ and the number of edges labeled with $1$ differ by at most $1$. In this paper, we study power cordial labeling and investigate power cordial labeling for some standard graph families.