Results 41 to 50 of about 891,390 (207)

On the inverse mostar index problem for molecular graphs [PDF]

Transactions on Combinatorics
Mostar indices are recently proposed distance-based graph invariants, that already have been much investigated and found applications. In this paper, we investigate the inverse problem for Mostar indices of unicyclic and bicyclic molecular graphs.
Liju Alex, Ivan Gutman
doaj   +1 more source

The Ordering of the Unicyclic Graphs with respect to Largest Matching Root with Given Matching Number

Journal of Mathematics, 2022
The matching roots of a simple connected graph G are the roots of the matching polynomial which is defined as MGx=∑k=0n/2−1kmG,kxn−2k, where mG,k is the number of the k matchings of G. Let λ1G denote the largest matching root of the graph G.
Luozhong Gong, Weijun Liu
doaj   +1 more source

Graphs with mixed metric dimension three and related algorithms

AIMS Mathematics, 2023
Let $ G = (V, E) $ be a simple connected graph. A vertex $ x\in V(G) $ resolves the elements $ u, v\in E(G)\cup V(G) $ if $ d_G(x, u)\neq d_G(x, v) $.
Dalal Awadh Alrowaili , Uzma Ahmad , Saira Hameeed, Muhammad Javaid   +3 more
doaj   +1 more source

Laplacian integral signed graphs with few cycles

AIMS Mathematics, 2023
A connected graph with n vertices and m edges is called k-cyclic graph if k=m−n+1. We call a signed graph is Laplacian integral if all eigenvalues of its Laplacian matrix are integers.
Dijian Wang, Dongdong Gao
doaj   +1 more source

A Comparison between the Zero Forcing Number and the Strong Metric Dimension of Graphs [PDF]

, 2014
The \emph{zero forcing number}, $Z(G)$, of a graph $G$ is the minimum cardinality of a set $S$ of black vertices (whereas vertices in $V(G)-S$ are colored white) such that $V(G)$ is turned black after finitely many applications of "the color-change rule":
A Sebö, CJ Edholm, CX Kang, CX Kang, D Burgarth, D Burgarth, DD Row, E Yi, F Barioli, F Barioli, F Harary, G Chartrand, K Chilakamarri, L Eroh, L Hogben, MR Garey, OR Oellermann, PJ Slater, S Khuller, S Severini   +19 more
core   +1 more source

The local multiset dimension of unicyclic graph

IOP Conference Series: Earth and Environment, 2019
An unicyclic graph is a graph which contains exactly one cycle. For k–ordered set W = {s1, s2, . . ., sk} of vertex set G, the multiset representation of a vertex v of G with respect to W is rm(v|W ) = {d(v, s1), d(v, s2), . . ., d(v, sk)} where d(v, si)
R. Adawiyah, Dafik, R. Prihandini, E. R. Albirri, I. H. Agustin, R. Alfarisi   +5 more
semanticscholar   +1 more source

On Critical Unicyclic Graphs with Cutwidth Four

AppliedMath, 2022
The cutwidth minimization problem consists of finding an arrangement of the vertices of a graph G on a line Pn with n=|V(G)| vertices in such a way that the maximum number of overlapping edges (i.e., the congestion) is minimized.
Zhenkun Zhang, Hongjian Lai
doaj   +1 more source

Introducing New Exponential Zagreb Indices for Graphs

Journal of Mathematics, 2021
New graph invariants, named exponential Zagreb indices, are introduced for more than one type of Zagreb index. After that, in terms of exponential Zagreb indices, lists on equality results over special graphs are presented as well as some new bounds on ...
Nihat Akgunes, Busra Aydin
doaj   +1 more source

Extremal Unicyclic Graphs With Minimal Distance Spectral Radius

Discussiones Mathematicae Graph Theory, 2014
The distance spectral radius ρ(G) of a graph G is the largest eigenvalue of the distance matrix D(G). Let U (n,m) be the class of unicyclic graphs of order n with given matching number m (m ≠ 3).
Lu Hongyan, Luo Jing, Zhu Zhongxun
doaj   +1 more source

Spanning trees and even integer eigenvalues of graphs [PDF]

, 2014
For a graph $G$, let $L(G)$ and $Q(G)$ be the Laplacian and signless Laplacian matrices of $G$, respectively, and $\tau(G)$ be the number of spanning trees of $G$.
Ghorbani, Ebrahim
core   +1 more source