todeschini et al. have recently suggested to consider multiplicative variants of additive graphinvariants, which applied to the zagreb indices would lead to the multiplicative zagrebindices of a graph g, denoted by ( ) 1  g and ( ) 2  g , under the name first and secondmultiplicative zagreb index, respectively. these are define as  ( )21 ( ) ( )v v gg g d vand ( ) ( ) ( )( )2 g d v d v gu...

‎    The Narumi-Katayama index is the first topological index defined by the product of some graph theoretical quantities. Let G be a simple graph. Narumi-Katayama index of G is defined as the product of the degrees of the vertices of G. In this paper, we define the Narumi-Katayama polynomial of G. Next, we investigate some properties of this polynomial for graphs and then, we obtain ...

Optimization and reduction of costs in management of distribution and transportation of commodity are one of the main goals of many organizations. Using suitable models in supply chain in order to increase efficiency and appropriate location for support centers in logistical networks is highly important for planners and managers. Graph modeling can be used to analyze these problems and many oth...

The general sum-connectivity index of a graph $G$ is defined as $chi_{alpha}(G)= sum_{uvin E(G)} (d_u + d_{v})^{alpha}$ where $d_{u}$ is degree of the vertex $uin V(G)$, $alpha$ is a real number different from $0$ and $uv$ is the edge connecting the vertices $u,v$. In this note, the problem of characterizing the graphs having extremum $chi_{alpha}$ values from a certain collection of polyomino ...

We present a new family of graphical models that may have undirected, directed and bidirected edges. We name these new models marginal AMP (MAMP) chain graphs because each of them can be seen as the result of marginalizing out some nodes in an AMP chain graph. However, MAMP chain graphs do not only subsume AMP chain graphs but also regression chain graphs. We describe global and local Markov pr...

Chain graphs are exactly bipartite graphs without induced 2K 2 (a graph with four vertices and two disjoint edges). A graph G = (V, E) with a given independent set S ⊆ V (a set of pairwise non-adjacent vertices) is said to be a chain partitioned probe graph if G can be extended to a chain graph by adding edges between certain vertices in S. In this note we give two characterizations for chain p...