In this paper we obtain an upper bound and also a lower bound for maximum edges of strongly 2 multiplicative graphs of order n. Also we prove that triangular ladder the graph obtained by duplication of an arbitrary edge by a new vertex in path and the graphobtained by duplicating all vertices by new edges in a path and some other graphs are strongly 2 multiplicative

The Harmonic index $ H(G) $ of a graph $ G $ is defined as the sum of the weights $ dfrac{2}{d(u)+d(v)} $ of all edges $ uv $ of $G$, where $d(u)$ denotes the degree of the vertex $u$ in $G$. In this work, we prove the conjecture $dfrac{H(G)}{D(G)} geq dfrac{1}{2}+dfrac{1}{3(n-1)}  $ given by Jianxi Liu in 2013 when G is a unicyclic graph and give a better bound $ dfrac{H(G)}{D(G)}geq dfra...

Abstract—Keyword Search is known as a user-friendly alternative for structured languages to retrieve information from graph-structured data. Efficient retrieving of relevant answers to a keyword query and effective ranking of these answers according to their relevance are two main challenges in the keyword search over graph-structured data. In this paper, a novel scoring function is proposed, w...

many graph theoretical parameters have been used to describe the vulnerability of communication networks, including toughness, binding number, rate of disruption, neighbor-connectivity, integrity, mean integrity, edgeconnectivity vector, l-connectivity and tenacity. in this paper we discuss integrity and its properties in vulnerability calculation. the integrity of a graph g, i(g), is defined t...

Understanding the evolutionary mechanisms of dynamic graphs is crucial since a basic characteristic real-world networks. The challenges modeling are as follows: (1) Real-world dynamics frequently characterized by group effects, which essentially emerge from high-order interactions involving groups entities. Therefore, pairwise revealed edges insufficient to describe complex systems. (2) graph d...