%0 Journal Article
%T On strongly 2-multiplicative graphs
%J Communications in Combinatorics and Optimization
%I Azarbaijan Shahid Madani University
%Z 2538-2128
%A Somashekara, D.D.
%A Ravi, H.E.
%A Veena, C.R.
%D 2020
%\ 12/01/2020
%V 5
%N 2
%P 179-190
%! On strongly 2-multiplicative graphs
%K graph labeling
%K strongly 2-multiplicative
%K types of graphs
%R 10.22049/cco.2020.26647.1127
%X A simple connected graph $G$ of order $nge 3$ 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.
%U http://comb-opt.azaruniv.ac.ir/article_14028_5ef7f3d3936254933ebe84c316170400.pdf