We introduce new distance measures for comparing straight-line embedded graphs based on the Fréchet and weak distance. These graph distances are defined using continuous mappings thus take combinatorial structure as well geometric embeddings of into account. present a general algorithmic approach computing these distances. Although we show that deciding is NP-hard graphs, prove our yields polyn...

A perfect matching in a graph G is set of nonadjacent edges covering every vertex G. Motivated by recent progress on the relations between eigenvalues and number graph, this paper, we aim to present distance spectral radius condition guarantee existence matching. Let be an n-vertex connected where n even λ1(D(G)) Then following statements are true. (I) If 4≤n≤8 λ1(DG)≤λ1(D(Sn,n2−1)), then conta...

We generalize several topological indices and introduce the general degree distance of a connected graph $G$. For $a, b \in \mathbb{R}$, $DD_{a,b} (G) = \sum_{ v V(G)} [deg_{G}(v)]^a S^b_{G} (v)$, where $V(G)$ is vertex set $G$, $deg_G (v)$ $v$, $S^b_{G} (v) w V(G) \setminus \{ \} } [d_{G} (v,w) ]^{b}$ $d_{G} (v,w)$ between $v$ $w$ in present some sharp bounds on for multipartite graphs trees g...