AU - Gao, Zh.-B.
AU - Han, R.-Y.
AU - Lee, S.-M.
AU - Ren, H.-N.
AU - Lau, G.-Ch.
TI - Labeling Subgraph Embeddings and Cordiality of Graphs
PT - JOURNAL ARTICLE
TA - IJMSI
JN - IJMSI
VO - 14
VI - 2
IP - 2
4099 - http://ijmsi.ir/article-1-925-en.html
4100 - http://ijmsi.ir/article-1-925-en.pdf
SO - IJMSI 2
ABĀ - Let $G$ be a graph with vertex set $V(G)$ and edge set $E(G)$, a vertex labeling $f : V(G)rightarrow mathbb{Z}_2$ induces an edge labeling $ f^{+} : E(G)rightarrow mathbb{Z}_2$ defined by $f^{+}(xy) = f(x) + f(y)$, for each edge $ xyin E(G)$. For each $i in mathbb{Z}_2$, let $ v_{f}(i)=|{u in V(G) : f(u) = i}|$ and $e_{f^+}(i)=|{xyin E(G) : f^{+}(xy) = i}|$. A vertex labeling $f$ of a graph $G$ is said to be friendly if $| v_{f}(1)-v_{f}(0) | leq 1$. The friendly index set of the graph $G$, denoted by $FI(G)$, is defined as ${|e_{f^+}(1) - e_{f^+}(0)|$ : the vertex labeling $f$ is friendly$}$. The full friendly index set of the graph $G$, denoted by $FFI(G)$, is defined as ${e_{f^+}(1) - e_{f^+}(0)$ : the vertex labeling $f$ is friendly$}$. A graph $G$ is cordial if $-1, 0$ or $1in FFI(G)$. In this paper, by introducing labeling subgraph embeddings method, we determine the cordiality of a family of cubic graphs which are double-edge blow-up of $P_2times P_n, nge 2$. Consequently, we completely determined friendly index and full product cordial index sets of this family of graphs.
CP - IRAN
IN - KM12, Jalan Muar, Segamat, Johor, Malaysia
LG - eng
PB - IJMSI
PG - 79
PT - Research paper
YR - 2019