On graphs with algebraic connectivity equal to minimum edge density
نویسندگان
چکیده
منابع مشابه
Tricyclic and Tetracyclic Graphs with Maximum and Minimum Eccentric Connectivity
Let $G$ be a connected graph on $n$ vertices. $G$ is called tricyclic if it has $n + 2$ edges, and tetracyclic if $G$ has exactly $n + 3$ edges. Suppose $mathcal{C}_n$ and $mathcal{D}_n$ denote the set of all tricyclic and tetracyclic $n-$vertex graphs, respectively. The aim of this paper is to calculate the minimum and maximum of eccentric connectivity index in $mathcal{C}_n$ and $mathcal{D}_n...
متن کاملOn the edge-connectivity of C_4-free graphs
Let $G$ be a connected graph of order $n$ and minimum degree $delta(G)$.The edge-connectivity $lambda(G)$ of $G$ is the minimum numberof edges whose removal renders $G$ disconnected. It is well-known that$lambda(G) leq delta(G)$,and if $lambda(G)=delta(G)$, then$G$ is said to be maximally edge-connected. A classical resultby Chartrand gives the sufficient condition $delta(G) geq frac{n-1}{2}$fo...
متن کاملEla the Minimum Algebraic Connectivity of Caterpillar Unicyclic Graphs
A caterpillar unicyclic graph is a unicyclic graph in which the removal of all pendant vertices makes it a cycle. In this paper, the unique caterpillar unicyclic graph with minimum algebraic connectivity among all caterpillar unicyclic graphs is determined.
متن کاملOn the Minimum Degree, Edge-connectivity and Connectivity of Power Graphs of Finite Groups
The power graph of a group G is the graph whose vertex set is G and two distinct vertices are adjacent if one is a power of the other. In this paper, the minimum degree of power graphs of certain classes of cyclic groups, abelian p-groups, dihedral groups and dicyclic groups are obtained. It is ascertained that the edge-connectivity and minimum degree of power graphs are equal, and consequently...
متن کاملAlgebraic Connectivity of Graphs, with Applications
The analysis of matrices associated with discrete, pairwise comparisons can be a very useful toolbox for a computer scientist. In particular, Spectral Graph Theory is based on the observation that eigenvalues and eigenvectors of these matrices betray a lot of properties of graphs associated with them. The first major section of this paper is a survey of key results in Spectral Graph Theory. The...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Linear Algebra and its Applications
سال: 2003
ISSN: 0024-3795
DOI: 10.1016/s0024-3795(02)00538-4