منابع مشابه
On the spectral radii of quasi-tree graphs and quasi-unicyclic graphs with k pendent vertices
A connected graph G = (V, E) is called a quasi-tree graph if there exists a vertex u0 ∈ V (G) such that G−u0 is a tree. A connected graph G = (V, E) is called a quasi-unicyclic graph if there exists a vertex u0 ∈ V (G) such that G− u0 is a unicyclic graph. Set T (n, k) := {G : G is a n-vertex quasi-tree graph with k pendant vertices}, and T (n, d0, k) := {G : G ∈ T (n, k) and there is a vertex ...
متن کاملInfinite paths in planar graphs I: Graphs with radial nets
Let G be an infinite 4-connected planar graph such that the deletion of any finite set of vertices from G results in exactly one infinite component. Dean et al proved that either G admits a radial net or a special subgraph of G admits a ladder net, and they used these nets to show that G contains a spanning 1-way infinite path. In this paper, we show that if G admits a radial net, then G also c...
متن کاملOn Merrifield-Simmons index of unicyclic graphs with given girth and prescribed pendent vertices
For a graph G, the Merrifield-Simmons index i(G) is defined as the total number of independent sets of the graph G. Let G(n, l, k) be the class of unicyclic graphs on n vertices with girth and pendent vertices being resp. l and k. In this paper, we characterize the unique unicyclic graph possessing prescribed girth and pendent vertices with the maximal Merrifield-Simmons index among all graphs ...
متن کاملComplete Bipartite Graphs with No Rainbow Paths
Motivated by questions in Ramsey theory, Thomason and Wagner described the edge colorings of complete graphs that contain no rainbow path Pt of order t. In this paper, we consider the edge colorings of complete bipartite graphs that contain no rainbow path Pt. Mathematics Subject Classification: 05C15, 05C38, 05C55
متن کاملCovering partially directed graphs with directed paths
We consider graphs which contain both directed and undirected edges (partially directed graphs). We show that the problem of covering the edges of such graphs with a minimum number of edge-disjoint directed paths respecting the orientations of the directed edges is polynomially solvable.We exhibit a good characterization for this problem in the form of a min–max theorem.We introduce a more gene...
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: Electronic Journal of Graph Theory and Applications
سال: 2020
ISSN: 2338-2287
DOI: 10.5614/ejgta.2020.8.2.8