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Unicyclic Graphs

Ordering of Unicyclic Graphs with Perfect Matchings by Minimal Matching Energies

Ordering of Unicyclic Graphs with Perfect Matchings by Minimal Matching Energies

... the unicyclic graphs with the minimal and maximal matching ...the unicyclic graphs with the first eight minimal matching ...bipartite unicyclic graphs with the first   ( n − 3 ...

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On unicyclic graphs of metric dimension \(2\)

On unicyclic graphs of metric dimension \(2\)

... of unicyclic graphs some bounds were ...of graphs (e.g. [7], [8]). The third way is a description of graphs having a fixed value of metric ...

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On Harmonic Index and Diameter of Unicyclic Graphs

On Harmonic Index and Diameter of Unicyclic Graphs

... connected graphs, trees and unicyclic graphs and characterized the corresponding extremal ...special graphs namely ladder graph, prism graph and book ...

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On the Eccentric Connectivity Index of Unicyclic Graphs

On the Eccentric Connectivity Index of Unicyclic Graphs

... In this paper, we obtain the upper and lower bounds on the eccentricity connectivity index of unicyclic graphs with perfect matchings. Also we give some lower bounds on the eccentric connectivity index of ...

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Minimal skew energy of oriented unicyclic graphs with a perfect matching

Minimal skew energy of oriented unicyclic graphs with a perfect matching

... 4 Minimal skew energy of oriented unicyclic graphs with a perfect matching In this section, we always assume that the order of a graph is n = k. A k-matching is a disjoint union of k edges in G. The number ...

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Spectral properties of a class of unicyclic graphs

Spectral properties of a class of unicyclic graphs

... A unicyclic graph is called fully loaded if every vertex on its unique cycle has degree at least ...loaded unicyclic graphs, where n ≥ ...the graphs with the kth maximum spectral radius among ...

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Ordering non bipartite unicyclic graphs with pendant vertices by the least Q eigenvalue

Ordering non bipartite unicyclic graphs with pendant vertices by the least Q eigenvalue

... The rest of the paper is organized as follows. In Section , we recall some basic notions and lemmas used further, and prove two new lemmas. In Section , we order non-bipartite unicyclic graphs of order n ...

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The Signless Laplacian Estrada Index of Unicyclic Graphs

The Signless Laplacian Estrada Index of Unicyclic Graphs

... the unicyclic graphs with the first two largest and smallest SLEE’s and then determine the unique unicyclic graph with maximum SLEE among all unicyclic graphs on n vertices with a given ...

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The second geometric-arithmetic index for trees and unicyclic graphs

The second geometric-arithmetic index for trees and unicyclic graphs

... where denotes the number of vertices in lying closer to u than to . In this paper we find a sharp upper bound for ( ), where T is tree, in terms of the order and maximum degree of the tree. We also find a sharp upper ...

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Ordering the oriented unicyclic graphs whose skew spectral radius is bounded by 2

Ordering the oriented unicyclic graphs whose skew spectral radius is bounded by 2

... a unicyclic graph. In this paper, the structure of oriented unicyclic graphs whose skew-spectral radius does not exceed 2 is ...oriented unicyclic graphs with n vertices whose ...

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On unicyclic graphs of metric dimension 2 with vertices of degree 4

On unicyclic graphs of metric dimension 2 with vertices of degree 4

... a unicyclic graph with metric dimension 2 and {a, b} is a metric basis of G then the degree of any vertex v of G is at most 4 and degrees of both a and b are at most ...semiunispider graphs and their ...

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Szeged index of bipartite unicyclic graphs

Szeged index of bipartite unicyclic graphs

... n e G n e G over all edges e  uv of G , where n e G 1 ( | ) and n e G 2 ( | ) are respectively the number of vertices of G lying closer to vertex u than to vertex v and the number of vertices of G lying closer to vertex ...

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Ordering Unicyclic Graphs in Terms of Their Smaller Least Eigenvalues

Ordering Unicyclic Graphs in Terms of Their Smaller Least Eigenvalues

... Research Article Ordering Unicyclic Graphs in Terms of Their Smaller Least Eigenvalues Guang-Hui Xu Department of Applied Mathematics, Zhejiang A&F University, Hangzhou 311300, China Cor[r] ...

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A Note on the Nullity of Unicyclic Graphs

A Note on the Nullity of Unicyclic Graphs

... η > . This question is of great interest in chemistry, because, as has been shown in [2], for a bipartite graph G (corresponding to an alternant hydrocarbon), if η ( ) G > 0 , then it indicates the molecule which ...

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Minimal skew energy of oriented unicyclic graphs with fixed diameter

Minimal skew energy of oriented unicyclic graphs with fixed diameter

... oriented unicyclic graphs. Below, we focus on the graphs with order at least , since the skew energy of an ori- ented graph with a small order can be calculated directly by mathematical software ...

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On the sum of the two largest Laplacian eigenvalues of unicyclic graphs

On the sum of the two largest Laplacian eigenvalues of unicyclic graphs

... MSC: 05C50; 15A48 Keywords: Laplacian eigenvalue; sum of eigenvalues; largest eigenvalue; unicyclic graph.. Its order is |V G|, denoted by nG or n for short, and its size is |EG|, denote[r] ...

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On (Semi-) Edge-primality of Graphs

On (Semi-) Edge-primality of Graphs

... tree graphs have a prime vertex labeling (Entringer-Tout Conjecture); (2) All unicyclic graphs have a prime vertex labeling (Seoud and Youssef ...

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On the revised edge-Szeged index of graphs

On the revised edge-Szeged index of graphs

... of unicyclic graphs and using this result we identify the minimum revised edge- Szeged index of conjugated unicyclic graphs which is defined as the unicyclic graphs with a ...

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On the least signless Laplacian eigenvalue of a non bipartite connected graph with fixed maximum degree

On the least signless Laplacian eigenvalue of a non bipartite connected graph with fixed maximum degree

... non-bipartite unicyclic graphs of order n with maximum degree and among all non-bipartite connected graphs of order n with maximum degree , ...

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On the Absolute Sum of Chromatic
Polynomial Coefficient of Graphs

On the Absolute Sum of Chromatic Polynomial Coefficient of Graphs

... of graphs, see related references ...completed graphs, and obtained the sharp upper and lower bounds for the absolute sum of chromatic polynomial coefficients of any connected ...q-tree, unicyclic ...

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