Online graph exploration on trees, unicyclic graphs and cactus graphs
نویسندگان
چکیده
منابع مشابه
Leap Zagreb indices of trees and unicyclic graphs
By d(v|G) and d_2(v|G) are denoted the number of first and second neighborsof the vertex v of the graph G. The first, second, and third leap Zagreb indicesof G are defined asLM_1(G) = sum_{v in V(G)} d_2(v|G)^2, LM_2(G) = sum_{uv in E(G)} d_2(u|G) d_2(v|G),and LM_3(G) = sum_{v in V(G)} d(v|G) d_2(v|G), respectively. In this paper, we generalizethe results of Naji et al. [Commun. Combin. Optim. ...
متن کاملThe second geometric-arithmetic index for trees and unicyclic graphs
Let $G$ be a finite and simple graph with edge set $E(G)$. The second geometric-arithmetic index is defined as $GA_2(G)=sum_{uvin E(G)}frac{2sqrt{n_un_v}}{n_u+n_v}$, where $n_u$ denotes the number of vertices in $G$ lying closer to $u$ than to $v$. In this paper we find a sharp upper bound for $GA_2(T)$, where $T$ is tree, in terms of the order and maximum degree o...
متن کاملThe Hyper-Zagreb Index of Trees and Unicyclic Graphs
Topological indices are widely used as mathematical tools to analyze different types of graphs emerged in a broad range of applications. The Hyper-Zagreb index (HM) is an important tool because it integrates the first two Zagreb indices. In this paper, we characterize the trees and unicyclic graphs with the first four and first eight greatest HM-value, respectively.
متن کاملRevolutionaries and spies on trees and unicyclic graphs
A team of r revolutionaries and a team of s spies play a game on a graph G. Initially, revolutionaries and then spies take positions at vertices. In each subsequent round, each revolutionary may move to an adjacent vertex or not move, and then each spy has the same option. The revolutionaries want to hold an unguarded meeting, meaning m revolutionaries at some vertex having no spy at the end of...
متن کاملThe 3-path-step Operator on Trees and Unicyclic Graphs
E.Prisner in his book Graph Dynamics defines the k-path-step operator on the class of finite graphs. The k-path-step operator (for a positive integer k) is the operator S′ k which to every finite graph G assigns the graph S′ k(G) which has the same vertex set as G and in which two vertices are adjacent if and only if there exists a path of length k in G connecting them. In the paper the trees a...
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ژورنال
عنوان ژورنال: Information Processing Letters
سال: 2021
ISSN: 0020-0190
DOI: 10.1016/j.ipl.2021.106096