TY - JOUR ID - 14028 TI - On strongly 2-multiplicative graphs JO - Communications in Combinatorics and Optimization JA - CCO LA - en SN - 2538-2128 AU - Somashekara, D.D. AU - Ravi, H.E. AU - Veena, C.R. AD - Department of Studies in Mathematics, University of Mysore Manasagangotri, Mysore-570006, India AD - Department of Studies in Mathematics, University of Mysore, Manasagangotri, Mysore-570006 AD - Department of Mathematics, JSS College of Arts, Commerce and Science, Mysore-570025, India Y1 - 2020 PY - 2020 VL - 5 IS - 2 SP - 179 EP - 190 KW - graph labeling KW - strongly 2-multiplicative KW - types of graphs DO - 10.22049/cco.2020.26647.1127 N2 - 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.  UR - http://comb-opt.azaruniv.ac.ir/article_14028.html L1 - http://comb-opt.azaruniv.ac.ir/article_14028_5ef7f3d3936254933ebe84c316170400.pdf ER -