Acyclic and unicyclic graphs whose minimum skew rank is equal to the minimum skew rank of a diametrical path

Algorithms for Computing Wiener Indices of Acyclic and Unicyclic Graphs

Let $G=(V(G),E(G))$ be a molecular graph, where $V(G)$ and $E(G)$ are the sets of vertices (atoms) and edges (bonds). A topological index of a molecular graph is a numerical quantity which helps to predict the chemical/physical properties of the molecules. The Wiener, Wiener polarity and the terminal Wiener indices are the distance based topological indices. In this paper, we described a linear time algorithm {\bf(LTA)} that computes the Wiener index for acyclic graphs and extended this algorithm for unicyclic graphs. The same algorithms are modified to compute the terminal Wiener index and th…

强单圈和强双圈图序列

Forcibly unicyclic and bicyclic graphic sequences

本文研究图序列的强性质，旨在刻画强单圈和强双圈图序列，即所有具有该度序列的图均为连通且边数分别为 n 或 n+1 的图。

Forbidden Subgraphs in Connected Graphs

Given a set $ξ=\{H_1,H_2,...\}$ of connected non acyclic graphs, a $ξ$-free graph is one which does not contain any member of $% ξ$ as copy. Define the excess of a graph as the difference between its number of edges and its number of vertices. Let ${\gr{W}}_{k,ξ}$ be theexponential generating function (EGF for brief) of connected $ξ$-free graphs of excess equal to $k$ ($k \geq 1$). For each fixed $ξ$, a fundamental differential recurrence satisfied by the EGFs ${\gr{W}}_{k,ξ}$ is derived. We give methods on how to solve this nonlinear recurrence for the first few values of $k$ by means of grap…