Results 21 to 30 of about 580,793 (206)
Online graph exploration on trees, unicyclic graphs and cactus graphs [PDF]
Information Processing Letters, 2021 We study the problem of exploring all vertices of an undirected weighted graph that is initially unknown to the searcher. An edge of the graph is only revealed when the searcher visits one of its endpoints. Beginning at some start node, the searcher's goal is to visit every vertex of the graph before returning to the start node on a tour as short as ...
Fritsch, Robin
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Stable and semi-stable unicyclic graphs [PDF]
Discrete Mathematics, 1974 AbstractWe show by a constructive proof, that if a unicyclic graph has a transposition in its automorphism group, then it is stable. Using a similar technique, we also determine which unicyclic graphs are not semi-stable.
K. L. McAvaney +2 more
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Resolving an Open Problem on the Exponential Arithmetic–Geometric Index of Unicyclic Graphs
MathematicsRecently, the exponential arithmetic–geometric index (EAG) was introduced. The exponential arithmetic–geometric index (EAG) of a graph G is defined as EAG(G)=∑vivj∈E(G)edi+dj2didj, where di represents the degree of the vertex vi in G.
Kinkar Chandra Das, Jayanta Bera
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Minor-obstructions for apex sub-unicyclic graphs
, 2020 International audienceA graph is {\em sub-unicyclic} if it contains at most one cycle. A graph $G$ is {\em $k$-apex sub-unicyclic} if it can become sub-unicyclic by removing $k$ of its vertices.
Velona, Vasiliki +5 more
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High-ordered spectral characterization of unicyclic graphs [PDF]
, 2022 In this paper we will apply the tensor and its traces to investigate the spectral characterization of unicyclic graphs. Let $G$ be a graph and $G^m$ be the $m$-th power (hypergraph) of $G$.
Fan, Yi-Zheng +2 more
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The inverse of the incidence matrix of a unicyclic graph [PDF]
Linear and Multilinear Algebra, 2022 The vertex-edge incidence matrix of a (connected) unicyclic graph G is a square matrix which is invertible if and only if the cycle of G is an odd cycle. A combinatorial formula of the inverse of the incidence matrix of an odd unicyclic graph was known.
Hessert, Ryan, Mallik, Sudipta
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Generating graceful unicyclic graphs from a given forest
AKCE International Journal of Graphs and Combinatorics, 2020 Acharya (1982) proved that every connected graph can be embedded in a graceful graph. The generalization of this result that, any set of graphs can be packed into a graceful graph was proved by Sethuraman and Elumalai (2005). Recently, Sethuraman et al. (
G. Sethuraman, V. Murugan
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ALGORITHMIC ASPECTS OF ROMAN GRAPHS [PDF]
Journal of Algebraic Systems, 2021 Let $G=(V, E)$ be a graph. A set $S \subseteq V$ is called a dominating set of $G$ if for every $v\in V-S$ there is at least one vertex $u \in N(v)$ such that $u\in S$.
A. Poureidi
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Binomial edge ideals of unicyclic graphs [PDF]
International Journal of Algebra and Computation, 2021 Let [Formula: see text] be a connected graph on the vertex set [Formula: see text]. Then [Formula: see text]. In this paper, we prove that if [Formula: see text] is a unicyclic graph, then the depth of [Formula: see text] is bounded below by [Formula: see text]. Also, we characterize [Formula: see text] with [Formula: see text] and [Formula: see text].
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Unicyclic graphs with bicyclic inverses [PDF]
, 2017 A graph is nonsingular if its adjacency matrix A(G) is nonsingular. The inverse of a nonsingular graph G is a graph whose adjacency matrix is similar to A(G)−1 via a particular type of similarity. Let H denote the class of connected bipartite graphs with
Swarup Kumar Panda, Panda, Swarup Kumar
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