the reverse degree distance of a connected graph $g$ is defined in discrete mathematical chemistry as [ r (g)=2(n-1)md-sum_{uin v(g)}d_g(u)d_g(u), ] where $n$, $m$ and $d$ are the number of vertices, the number of edges and the diameter of $g$, respectively, $d_g(u)$ is the degree of vertex $u$, $d_g(u)$ is the sum of distance between vertex $u$ and all other vertices of $g$, and $v(g)$ is the ...

The local boxicity of a graph G, denoted by lbox(G), is the minimum positive integer l such that G can be obtained using intersection k (where k≥l) interval graphs where each vertex appears as non-universal in at most these graphs. Let on n vertices having m edges. Δ denote maximum degree G. We show that, lbox(G)≤213log⁎⁡ΔΔ. lbox(G)∈O(nlog⁡n). lbox(G)≤(213log⁎⁡m+2)m. its product dimension. This...

in a graph g = (v,e), a subset s  v is said to be an open packing set if no two vertices of s have a common neighbour in g. the maximum cardinality of an open packing set is called the open packing number and is denoted by rho^o. this paper further studies on this parameter by obtaining some new bounds.