Polynomial graph invariants and linear hierarchies

2019 ◽  
Vol 74 (2) ◽  
pp. 366-368
Author(s):  
B. S. Bychkov ◽  
A. V. Mikhailov
Keyword(s):  
Graph Invariants ◽  
Linear Hierarchies

scholarly journals Topological Indices of Para-line Graphs of V-Phenylenic Nanostructures

2019 ◽  
Vol 17 (1) ◽  
pp. 260-266 ◽  
Author(s):  
Imran Nadeem ◽  
Hani Shaker ◽  
Muhammad Hussain ◽  
Asim Naseem
Keyword(s):  
Chemical Properties ◽  
Topological Indices ◽  
Structural Chemistry ◽  
Line Graphs ◽  
Physical And Chemical Properties ◽  
Graph Invariants ◽  
Molecular Graphs ◽  
Physical And Chemical ◽  
And Chemical Properties

Abstract The degree-based topological indices are numerical graph invariants which are used to correlate the physical and chemical properties of a molecule with its structure. Para-line graphs are used to represent the structures of molecules in another way and these representations are important in structural chemistry. In this article, we study certain well-known degree-based topological indices for the para-line graphs of V-Phenylenic 2D lattice, V-Phenylenic nanotube and nanotorus by using the symmetries of their molecular graphs.

Female, but not male, agonistic behaviour is associated with male reproductive success in stable bluebanded goby (Lythrypnus dalli) hierarchies

Behaviour ◽  
2014 ◽  
Vol 151 (10) ◽  
pp. 1367-1387 ◽  
Author(s):  
Tessa K. Solomon-Lane ◽  
Madelyne C. Willis ◽  
Devaleena S. Pradhan ◽  
Matthew S. Grober
Keyword(s):  
Reproductive Success ◽  
Egg Laying ◽  
Dominant Male ◽  
Male Reproductive Success ◽  
Agonistic Behaviour ◽  
Social Species ◽  
Evolution Of Sociality ◽  
Lythrypnus Dalli ◽  
Linear Hierarchies ◽  
Substantial Control

In many social species, there are important connections between social behaviour and reproduction that provide critical insights into the evolution of sociality. In this study, we describe associations between agonistic behaviour and male reproductive success in stable social groups of bluebanded gobies (Lythrypnus dalli). This highly social, sex-changing species forms linear hierarchies of a dominant male and multiple subordinate females. Males reproduce with each female in the harem and care for the eggs. Since aggression tends to be associated with reduced reproduction in social hierarchies, we hypothesized that males in groups with high rates of aggression would fertilise fewer eggs. We also hypothesized that a male’s agonistic behaviour would be associated with his reproductive success. Dominants often exert substantial control over their harem, including control over subordinate reproduction. To address these hypotheses, we quantified egg laying/fertilisation over 13 days and observed agonistic behaviour. We show that there was a significant, negative association between male reproductive success and the total rate agonistic interactions by a group. While no male behaviours were associated with the quantity of eggs fertilised, female agonistic behaviour may be central to male reproductive success. We identified a set of models approximating male reproductive success that included three female behaviours: aggression by the highest-ranking female and approaches by the lowest-ranking female were negatively associated with the quantity of eggs fertilised by males in their groups, but the efficiency with which the middle-ranking female displaced others was positively associated with this measure. These data provide a first step in elucidating the behavioural mechanisms that are associated with L. dalli reproductive success.

Some properties of subgroup complementary addition Cayley graphs on abelian groups

2021 ◽  
Author(s):  
Naveen Palanivel ◽  
Chithra A. Velu
Keyword(s):  
Cayley Graph ◽  
Abelian Groups ◽  
Cayley Graphs ◽  
Graph Invariants

In this paper, we introduce subgroup complementary addition Cayley graph [Formula: see text] and compute its graph invariants. Also, we prove that [Formula: see text] if and only if [Formula: see text] for all [Formula: see text] where [Formula: see text].

A Note on the Kirchhoff and Additive Degree-Kirchhoff Indices of Graphs

2015 ◽  
Vol 70 (6) ◽  
pp. 459-463 ◽  
Author(s):  
Yujun Yang ◽  
Douglas J. Klein
Keyword(s):  
Upper Bound ◽  
Extremal Graphs ◽  
Graph Invariants ◽  
Kirchhoff Index ◽  
Resistance Distance

AbstractTwo resistance-distance-based graph invariants, namely, the Kirchhoff index and the additive degree-Kirchhoff index, are studied. A relation between them is established, with inequalities for the additive degree-Kirchhoff index arising via the Kirchhoff index along with minimum, maximum, and average degrees. Bounds for the Kirchhoff and additive degree-Kirchhoff indices are also determined, and extremal graphs are characterised. In addition, an upper bound for the additive degree-Kirchhoff index is established to improve a previously known result.

scholarly journals Dominance relationships in a family pack of captive arctic wolves (Canis lupus arctos): the influence of competition for food, age and sex

PeerJ ◽  
2016 ◽  
Vol 4 ◽  
pp. e2707 ◽  
Author(s):  
Simona Cafazzo ◽  
Martina Lazzaroni ◽  
Sarah Marshall-Pescini
Keyword(s):  
Quantitative Methods ◽  
Social Dynamics ◽  
Dominance Relationships ◽  
The Social ◽  
Systematic Methodology ◽  
The Hierarchical Structure ◽  
Competition For Food ◽  
Linear Hierarchies ◽  
Feeding Context ◽  
Age And Sex

BackgroundDominance is one of the most pervasive concepts in the study of wolf social behaviour but recently its validity has been questioned. For some authors, the bonds between members of wolf families are better described as parent-offspring relationships and the concept of dominance should be used just to evaluate the social dynamics of non-familial captive pack members (e.g., Mech & Cluff, 2010). However, there is a dearth of studies investigating dominance relationships and its correlates in wolf family packs.MethodsHere, we applied a combination of the most commonly used quantitative methods to evaluate the dominance relationships in a captive family pack of 19 Arctic wolves.ResultsWe found a significant linear and completely transitive hierarchy based on the direction of submissive behaviours and found that dominance relationships were not influenced by the competitive contexts (feeding vs. non-feeding context). A significant linear hierarchy also emerges amongst siblings once the breeding pair (the two top-ranking individuals) is removed from analyses. Furthermore, results suggest that wolves may use greeting behaviour as a formal signal of subordination. Whereas older wolves were mostly dominant over younger ones, no clear effect of sex was found. However, frequency of agonistic (submissive, dominant and aggressive) behaviours was higher between female–female and male–male dyads than female–male dyads and sex-separated linear hierarchies showed a stronger linearity than the mixed one. Furthermore, dominance status was conveyed through different behavioural categories during intra-sexual and inter-sexual interactions.DiscussionCurrent results highlight the importance of applying a systematic methodology considering the individuals’ age and sex when evaluating the hierarchical structure of a social group. Moreover, they confirm the validity of the concept of dominance relationships in describing the social bonds within a family pack of captive wolves.

scholarly journals On Mostar and Edge Mostar Indices of Graphs

2021 ◽  
Vol 2021 ◽  
pp. 1-14
Author(s):  
Ali Ghalavand ◽  
Ali Reza Ashrafi ◽  
Mardjan Hakimi-Nezhaad
Keyword(s):  
Upper Bound ◽  
Graph Invariants ◽  
Open Questions ◽  
Bicyclic Graphs ◽  
Extremal Values

Let G be a graph with edge set E G and e = u v ∈ E G . Define n u e , G and m u e , G to be the number of vertices of G closer to u than to v and the number of edges of G closer to u than to v , respectively. The numbers n v e , G and m v e , G can be defined in an analogous way. The Mostar and edge Mostar indices of G are new graph invariants defined as M o G = ∑ u v ∈ E G n u u v , G − n v u v , G and M o e G = ∑ u v ∈ E G m u u v , G − m v u v , G , respectively. In this paper, an upper bound for the Mostar and edge Mostar indices of a tree in terms of its diameter is given. Next, the trees with the smallest and the largest Mostar and edge Mostar indices are also given. Finally, a recent conjecture of Liu, Song, Xiao, and Tang (2020) on bicyclic graphs with a given order, for which extremal values of the edge Mostar index are attained, will be proved. In addition, some new open questions are presented.

scholarly journals https://pisrt.org/psr-press/journals/easl-vol-2-issue-1-2019/degree-based-graph-invariants-for-the-molecular-graph-of-bismuth-tri-iodide/

2019 ◽  
Vol 2(2019) (1) ◽  
pp. 1-11 ◽  
Author(s):  
Zehui Shao ◽  
◽  
Abaid ur Rehman Virk ◽  
Muhammad Samar Javed ◽  
Mohammad Reza Farahani ◽  
...  
Keyword(s):  
Molecular Graph ◽  
Graph Invariants

scholarly journals Intersection dimension and graph invariants

2021 ◽  
Vol 41 (1) ◽  
pp. 153
Author(s):  
N.R. Aravind ◽  
C.R. Subramanian
Keyword(s):  
Graph Invariants

scholarly journals On relations between Kirchhoff index, Laplacian energy, Laplacian-energy-like invariant and degree deviation of graphs

Filomat ◽  
2020 ◽  
Vol 34 (3) ◽  
pp. 1025-1033
Author(s):  
Predrag Milosevic ◽  
Emina Milovanovic ◽  
Marjan Matejic ◽  
Igor Milovanovic
Keyword(s):  
Topological Index ◽  
Degree Sequence ◽  
Laplacian Matrix ◽  
Vertex Degree ◽  
Graph Invariants ◽  
Kirchhoff Index ◽  
Laplacian Eigenvalues ◽  
Laplacian Energy ◽  
Degree Deviation ◽  
Simple Connected Graph

Let G be a simple connected graph of order n and size m, vertex degree sequence d1 ? d2 ?...? dn > 0, and let ?1 ? ? 2 ? ... ? ?n-1 > ?n = 0 be the eigenvalues of its Laplacian matrix. Laplacian energy LE, Laplacian-energy-like invariant LEL and Kirchhoff index Kf, are graph invariants defined in terms of Laplacian eigenvalues. These are, respectively, defined as LE(G) = ?n,i=1 |?i-2m/n|, LEL(G) = ?n-1 i=1 ??i and Kf (G) = n ?n-1,i=1 1/?i. A vertex-degree-based topological index referred to as degree deviation is defined as S(G) = ?n,i=1 |di- 2m/n|. Relations between Kf and LE, Kf and LEL, as well as Kf and S are obtained.

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