The matroid is called loopless if the empty subset of E is closed, and is called a combinatorial geometry if in addition all single element subsets of E are closed. A closed subset of E is called a flat of M, and every subset of E has a well-defined rank and corank in the poset of all flats of M. The notion of matroid played a fundamental role in graph theory, coding theory, combinatorial optim...

Let G be a simple graph with vertex set V(G) and edge set E(G). For each a in V(G), let N(a) = {x E V(G) : ax E E(G)} be the set of neighbours of a. A subset S of V(G) is called a closed set of G if, for each pair of distinct elements u, b in S, N(a) ON(b) s S. Let Z’(G) be the family of closed sets of G, inclusive of the empty set 0. Evidently, Z(G) is closed under arbitrary intersection and i...

let $g$ be a connected graph, and let $d[g]$ denote the double graph of $g$. in this paper, we first derive closed-form formulas for different distance based topological indices for $d[g]$ in terms of that of $g$. finally, as illustration examples, for several special kind of graphs, such as, the complete graph, the path, the cycle, etc., the explicit formulas for some distance based topologica...