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On strongly 2-multiplicative graphs | ||
| Communications in Combinatorics and Optimization | ||
| مقاله 8، دوره 5، شماره 2، اسفند 2020، صفحه 179-190 اصل مقاله (418.92 K) | ||
| نوع مقاله: Original paper | ||
| شناسه دیجیتال (DOI): 10.22049/cco.2020.26647.1127 | ||
| نویسندگان | ||
| D.D. Somashekara1؛ H.E. Ravi* 2؛ C.R. Veena3 | ||
| 1Department of Studies in Mathematics, University of Mysore Manasagangotri, Mysore-570006, India | ||
| 2Department of Studies in Mathematics, University of Mysore, Manasagangotri, Mysore-570006 | ||
| 3Department of Mathematics, JSS College of Arts, Commerce and Science, Mysore-570025, India | ||
| چکیده | ||
| A simple connected graph $G$ of order $n\ge 3$ is a strongly 2-multiplicative if there is an injective mapping $f:V(G)\rightarrow \{1,2,\ldots,n\}$ such that the induced mapping $h:\mathcal{A} \rightarrow \mathbb{Z}^+$ defined by $h(\mathcal{P})= \prod_{i=1}^{3} f({v_j}_i)$, where $j_1,j_2,j_{3}\in \{1,2,\ldots,n\}$, and $\mathcal{P}$ is the path homotopy class of paths having the vertex set $\{ v_{j_1}, v_{j_2},v_{j_{3}} \}$, is injective. Let $\Lambda(n)$ be the number of distinct path homotopy classes in a strongly 2-multiplicative graph of order $n$. In this paper we obtain an upper bound and also a lower bound for $\Lambda(n)$. Also we prove that triangular ladder, $P_{2} \bigodot C_{n}$, $P_{m}\bigodot P_{n}$, the graph obtained by duplication of an arbitrary edge by a new vertex in path $P_{n}$ and the graph obtained by duplicating all vertices by new edges in a path $P_{n}$ are strongly 2-multiplicative. | ||
| کلیدواژه‌ها | ||
| graph labeling؛ strongly 2-multiplicative؛ types of graphs | ||
| مراجع | ||
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