Results 1 to 10 of about 1,782 (193)
Metric Dimensions of Bicyclic Graphs
Mathematics, 2023 The distance d(va,vb) between two vertices of a simple connected graph G is the length of the shortest path between va and vb. Vertices va,vb of G are considered to be resolved by a vertex v if d(va,v)≠d(vb,v).
Asad Khan +5 more
doaj +4 more sources
Characterization of the Minimizing Graph of the Connected Graphs Whose Complements Are Bicyclic [PDF]
Mathematics, 2017 In a certain class of graphs, a graph is called minimizing if the least eigenvalue of its adjacency matrix attains the minimum. A connected graph containing two or three cycles is called a bicyclic graph if its number of edges is equal to its number of ...
Muhammad Javaid
doaj +4 more sources
Bicyclic molecular graphs with the greatest energy [PDF]
Journal of the Serbian Chemical Society, 2008 The molecular graph Qn is obtained by attaching hexagons to the end vertices of the path graph Pn-12. Earlier empirical studies indicated that Qn has greatest energy among all bicyclic n-vertex (molecular) graphs.
IVAN GUTMAN +2 more
doaj +3 more sources
CONSTRUCTION OF BICYCLIC GRAPH AND ITS APPLICATION IN TRANS JOGJA ROUTES
Barekeng, 2023 A bicyclic graph is a type of graph that consists of exactly two cycles. A cycle is a graph that is a closed path where no vertices are repeated except the first and last vertices which are the same.
Aditya Ambarwati, Vira Hari Krisnawati
doaj +1 more source
Extremal Values of Variable Sum Exdeg Index for Conjugated Bicyclic Graphs
Journal of Chemistry, 2021 A connected graph GV,E in which the number of edges is one more than its number of vertices is called a bicyclic graph. A perfect matching of a graph is a matching in which every vertex of the graph is incident to exactly one edge of the matching set ...
Muhammad Rizwan +3 more
doaj +1 more source
Bicyclic Graphs with the Second-Maximum and Third-Maximum Degree Resistance Distance
Journal of Mathematics, 2021 Let G=V,E be a connected graph. The resistance distance between two vertices u and v in G, denoted by RGu,v, is the effective resistance between them if each edge of G is assumed to be a unit resistor.
Wenjie Ning, Kun Wang, Hassan Raza
doaj +1 more source
Iota energy orderings of bicyclic signed digraphs [PDF]
Transactions on Combinatorics, 2021 The concept of energy of a signed digraph is extended to iota energy of a signed digraph. The energy of a signed digraph $S$ is defined by $E(S)=\sum_{k=1}^n|{Re}(z_k)|$, where ${Re}(z_k)$ is the real part of eigenvalue $z_k$ and $z_k$ is the ...
Xiuwen Yang, Ligong Wang
doaj +1 more source
Maximum Reciprocal Degree Resistance Distance Index of Bicyclic Graphs
Discrete Dynamics in Nature and Society, 2021 The reciprocal degree resistance distance index of a connected graph G is defined as RDRG=∑u,v⊆VGdGu+dGv/rGu,v, where rGu,v is the resistance distance between vertices u and v in G. Let ℬn denote the set of bicyclic graphs without common edges and with n
Gaixiang Cai, Xing-Xing Li, Guidong Yu
doaj +1 more source
Bicyclic graphs with maximum sum of the two largest Laplacian eigenvalues
Journal of Inequalities and Applications, 2016 Let G be a simple connected graph and S 2 ( G ) $S_{2}(G)$ be the sum of the two largest Laplacian eigenvalues of G. In this paper, we determine the bicyclic graph with maximum S 2 ( G ) $S_{2}(G)$ among all bicyclic graphs of order n, which confirms the
Yirong Zheng +3 more
doaj +1 more source
Further Results on the Nullity of Signed Graphs
Journal of Applied Mathematics, 2014 The nullity of a graph is the multiplicity of the eigenvalue zero in its spectrum. A signed graph is a graph with a sign attached to each of its edges. In this paper, we apply the coefficient theorem on the characteristic polynomial of a signed graph and
Yu Liu, Lihua You
doaj +1 more source