On Bond Incident Degree Indices of Connected Graphs with Fixed Order and Number of Pendent Vertices
نویسندگان
چکیده
The graphs having the maximum value of certain bond incident degree indices (including second Zagreb index, general sum-connectivity and zeroth-order Randi? index) in class all connected with fixed order number pendent vertices are characterized this paper. problem finding minimum values index from aforementioned is also addressed. One obtained results about first has already been proved papers [I. Gutman, M. Kamran Jamil, N. Akhter, Trans. Combin. 4 (2015) 43-48] [M. Enteshari, B. Taeri, MATCH Commun. Math. Comput. Chem. 86 (2021) 17-28]; however, it here by another method a short proof. Moreover, one concerning gives partial solution to attacked aforementiond paper Enteshari Taeri.
منابع مشابه
graphs with fixed number of pendent vertices and minimal first zagreb index
the first zagreb index $m_1$ of a graph $g$ is equal to the sum of squaresof degrees of the vertices of $g$. goubko proved that for trees with $n_1$pendent vertices, $m_1 geq 9,n_1-16$. we show how this result can beextended to hold for any connected graph with cyclomatic number $gamma geq 0$.in addition, graphs with $n$ vertices, $n_1$ pendent vertices, cyclomaticnumber $gamma$, and minimal $m...
متن کاملMinimizing Degree-based Topological Indices for Trees with Given Number of Pendent Vertices∗
We derive sharp lower bounds for the first and the second Zagreb indices (M1 and M2 respectively) for trees and chemical trees with the given number of pendent vertices and find optimal trees. M1 is minimized by a tree with all internal vertices having degree 4, while M2 is minimized by a tree where each “stem” vertex is incident to 3 or 4 pendent vertices and one internal vertex, while the res...
متن کاملOn the extremal graphs with respect to bond incident degree indices
Many existing degree based topological indices can be clasified as bond incident degree (BID) indices, whose general form is BID(G) = ∑ uv∈E(G) Ψ(du, dv), where uv is the edge connecting the vertices u, v of the graph G, E(G) is the edge set of G, du is the degree of the vertex u and Ψ is a non-negative real valued (symmetric) function of du and dv. Here, it has been proven that if the extensio...
متن کاملOn the fixed number of graphs
A set of vertices $S$ of a graph $G$ is called a fixing set of $G$, if only the trivial automorphism of $G$ fixes every vertex in $S$. The fixing number of a graph is the smallest cardinality of a fixing set. The fixed number of a graph $G$ is the minimum $k$, such that every $k$-set of vertices of $G$ is a fixing set of $G$. A graph $G$ is called a $k$-fixed graph, if its fix...
متن کاملDistance spectral radius of trees with fixed number of pendent vertices
Article history: Received 16 October 2012 Accepted 25 June 2013 Available online 12 July 2013 Submitted by R. Brualdi
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Match
سال: 2022
ISSN: ['0340-6253']
DOI: https://doi.org/10.46793/match.88-3.625z