Ramsey and Gallai-Ramsey Numbers for Two Classes of Unicyclic Graphs
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DOI: 10.1007/s00373-020-02248-8
Abstract: Given a graph G and a positive integer k , define the Gallai-Ramsey number to be the minimum number of vertices n such that any k -edge coloring of $$K_n$$ K n contains either a… read more here.
Keywords: classes unicyclic; unicyclic graphs; two classes; ramsey ... See more keywords
Minimum Szeged index among unicyclic graphs with perfect matchings
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DOI: 10.1007/s10878-019-00390-5
Abstract: Let G be a connected graph. The Szeged index of G is defined as $$Sz(G)=\sum \nolimits _{e=uv\in E(G)}n_{u}(e|G)n_{v}(e|G)$$Sz(G)=∑e=uv∈E(G)nu(e|G)nv(e|G), where $$n_{u}(e|G)$$nu(e|G) (resp., $$n_{v}(e|G)$$nv(e|G)) is the number of vertices whose distance to vertex u (resp., v) is… read more here.
Keywords: index among; unicyclic graphs; minimum szeged; among unicyclic ... See more keywords
The Wiener index of unicyclic graphs given number of pendant vertices or cut vertices
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DOI: 10.1007/s12190-016-1022-y
Abstract: The Wiener index is the sum of distances between all pairs of distinct vertices in a connected graph, which is the oldest topological index related to molecular branching. In this article, we give a condition… read more here.
Keywords: index; unicyclic graphs; graphs given; wiener index ... See more keywords
On the largest eigenvalue of signed unicyclic graphs
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DOI: 10.1016/j.laa.2019.06.016
Abstract: Abstract Signed graphs are graphs whose edges get signs ±1 and, as for unsigned graphs, they can be studied by means of graph matrices. Here we focus our attention to the largest eigenvalue, also known… read more here.
Keywords: signed graphs; unicyclic graphs; eigenvalue signed; largest eigenvalue ... See more keywords
The extremal values of connective eccentricity index for trees and unicyclic graphs
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DOI: 10.1080/00207160.2015.1112003
Abstract: ABSTRACT Let G be a simple connected graph with vertex set . The connective eccentricity index (CEI) of a graph is defined as , where , denote the eccentricity and the degree of v, respectively.… read more here.
Keywords: trees unicyclic; unicyclic graphs; connective eccentricity; eccentricity ... See more keywords
Extremal unicyclic graphs with respect to the Sanskruti index
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DOI: 10.1142/s1793557120501478
Abstract: Sanskruti index of a graph [Formula: see text] with vertex-set [Formula: see text] and edge-set [Formula: see text] is [Formula: see text], where [Formula: see text]. In this paper, the extremal graphs in the class… read more here.
Keywords: formula see; sanskruti index; see text; unicyclic graphs ... See more keywords
Characterization of Extremal Unicyclic Graphs Using F-Coindex
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DOI: 10.1155/2021/8480971
Abstract: The study of forgotten index and coindex for the molecular structures of some special chemical graphs (compounds and drugs) has proven significant in medical and pharmaceutical drug design fields by making reliable statistical conclusion about… read more here.
Keywords: graphs; unicyclic graphs; graphs using; extremal unicyclic ... See more keywords
Spectral properties of a class of unicyclic graphs
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DOI: 10.1186/s13660-017-1367-2
Abstract: The eigenvalues of G are denoted by λ1(G),λ2(G),…,λn(G)$\lambda_{1}(G), \lambda_{2}(G), \ldots, \lambda_{n}(G)$, where n is the order of G. In particular, λ1(G)$\lambda _{1}(G)$ is called the spectral radius of G, λn(G)$\lambda_{n}(G)$ is the least eigenvalue of… read more here.
Keywords: properties class; lambda; unicyclic graphs; class unicyclic ... See more keywords
Characterization of Extremal Unicyclic Graphs with Fixed Leaves Using the Lanzhou Index
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DOI: 10.3390/sym14112408
Abstract: A topological index being a graph theoretic parameter plays a role of function for the assignment of a numerical value to a molecular graph which predicts the several physical and chemical properties of the underlying… read more here.
Keywords: index; class; unicyclic graphs; graph ... See more keywords