Iranian Journal of Mathematical Sciences and Informatics مجله علوم ریاضی و انفورماتیک IJMSI Basic Sciences http://ijmsi.ir 1 admin 1735-4463 2008-9473 8 7 14 8888 13 en jalali 1398 7 1 gregorian 2019 10 1 14 2 online 1 fulltext
en Labeling Subgraph Embeddings and Cordiality of Graphs تخصصي Special پژوهشي Research paper <p>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)\$.&nbsp; 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&nbsp; \${|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.</p> Vertex labeling, Full friendly index set, Cordiality, \$P_2\$-embeddings, \$C_4\$-embeddings. 79 92 http://ijmsi.ir/browse.php?a_code=A-10-2087-2&slc_lang=en&sid=1 Zh.-B. Gao gaozhenbin@aliyun.com 10031947532846006336 10031947532846006336 No Harbin Engineering University R.-Y. Han 3213358692@qq.com 10031947532846006337 10031947532846006337 No Harbin Engineering University S.-M. Lee sinminlee@gmail.com 10031947532846006338 10031947532846006338 No H.-N. Ren 1114912080@qq.com 10031947532846006339 10031947532846006339 No Harbin Engineering University G.-Ch. Lau geeclau@yahoo.com 10031947532846006340 10031947532846006340 Yes Universiti Teknologi MARA (Segamat Campus)