Pub Date : 2018-10-30DOI: 10.30538/PSRP-EASL2018.0005
M. C. M. Kumar, H. M. Nagesh, P. Humanities
For an arborescence Ar, a directed pathos total digraph Q = DPT (Ar) has vertex set V (Q) = V (Ar) ∪ A(Ar) ∪ P (Ar), where V (Ar) is the vertex set, A(Ar) is the arc set, and P (Ar) is a directed pathos set of Ar . The arc set A(Q) consists of the following arcs: ab such that a, b ∈ A(Ar) and the head of a coincides with the tail of b; uv such that u, v ∈ V (Ar) and u is adjacent to v; au (ua) such that a ∈ A(Ar) and u ∈ V (Ar) and the head (tail) of a is u; Pa such that a ∈ A(Ar) and P ∈ P (Ar) and the arc a lies on the directed path P ; PiPj such that Pi, Pj ∈ P (Ar) and it is possible to reach the head of Pj from the tail of Pi through a common vertex, but it is possible to reach the head of Pi from the tail of Pj . For this class of digraphs we discuss the planarity; outerplanarity; maximal outerplanarity; minimally nonouterplanarity; and crossing number one properties of these digraphs. The problem of reconstructing an arborescence from its directed pathos total digraph is also presented.
{"title":"Directed Pathos Total Digraph of an Arborescence","authors":"M. C. M. Kumar, H. M. Nagesh, P. Humanities","doi":"10.30538/PSRP-EASL2018.0005","DOIUrl":"https://doi.org/10.30538/PSRP-EASL2018.0005","url":null,"abstract":"For an arborescence Ar, a directed pathos total digraph Q = DPT (Ar) has vertex set V (Q) = V (Ar) ∪ A(Ar) ∪ P (Ar), where V (Ar) is the vertex set, A(Ar) is the arc set, and P (Ar) is a directed pathos set of Ar . The arc set A(Q) consists of the following arcs: ab such that a, b ∈ A(Ar) and the head of a coincides with the tail of b; uv such that u, v ∈ V (Ar) and u is adjacent to v; au (ua) such that a ∈ A(Ar) and u ∈ V (Ar) and the head (tail) of a is u; Pa such that a ∈ A(Ar) and P ∈ P (Ar) and the arc a lies on the directed path P ; PiPj such that Pi, Pj ∈ P (Ar) and it is possible to reach the head of Pj from the tail of Pi through a common vertex, but it is possible to reach the head of Pi from the tail of Pj . For this class of digraphs we discuss the planarity; outerplanarity; maximal outerplanarity; minimally nonouterplanarity; and crossing number one properties of these digraphs. The problem of reconstructing an arborescence from its directed pathos total digraph is also presented.","PeriodicalId":11518,"journal":{"name":"Engineering and Applied Science Letters","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2018-10-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42955218","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2018-10-30DOI: 10.30538/PSRP-EASL2018.0004
M. Imran, Asima Asghar, A. Q. Baig
The application of graph theory in chemical and molecular structure research far exceeds people’s expectations, and it has recently grown exponentially. In the molecular graph, atoms are represented by vertices and bonded by edges. In this report, we study the several Zagreb polynomials and Redefined Zagreb indices of Oxide Network.
{"title":"On Graph Invariants of Oxide Network","authors":"M. Imran, Asima Asghar, A. Q. Baig","doi":"10.30538/PSRP-EASL2018.0004","DOIUrl":"https://doi.org/10.30538/PSRP-EASL2018.0004","url":null,"abstract":"The application of graph theory in chemical and molecular structure research far exceeds people’s expectations, and it has recently grown exponentially. In the molecular graph, atoms are represented by vertices and bonded by edges. In this report, we study the several Zagreb polynomials and Redefined Zagreb indices of Oxide Network.","PeriodicalId":11518,"journal":{"name":"Engineering and Applied Science Letters","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2018-10-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49623717","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2018-10-30DOI: 10.30538/PSRP-EASL2018.0003
Wei Gao, Asima Asghar, W. Nazeer
Topological indices are numerical numbers associated with a graph that helps to predict many properties of underlined graph. In this paper we aim to compute multiplicative degree based topological indices of Jahangir graph.
{"title":"Computing Degree-Based Topological Indices of Jahangir Graph","authors":"Wei Gao, Asima Asghar, W. Nazeer","doi":"10.30538/PSRP-EASL2018.0003","DOIUrl":"https://doi.org/10.30538/PSRP-EASL2018.0003","url":null,"abstract":"Topological indices are numerical numbers associated with a graph that helps to predict many properties of underlined graph. In this paper we aim to compute multiplicative degree based topological indices of Jahangir graph.","PeriodicalId":11518,"journal":{"name":"Engineering and Applied Science Letters","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2018-10-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44852894","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2018-09-29DOI: 10.30538/PSRP-EASL2018.0001
Rachanna Kanabu, S. Hosamani
A carbon nanotube (CNT) is a miniature cylindrical carbon structure that has hexagonal graphite molecules attached at the edges. In this paper, we compute the numerical invariant (Topological indices) of linear [n]-phenylenic, lattice of C4C6C8[m,n], TUC4C6C8[m,n] nanotube, C4C6C8[m,n] nanotori.
{"title":"Some Numerical Invariants Associated with V-phenylenic Nanotube and Nanotori","authors":"Rachanna Kanabu, S. Hosamani","doi":"10.30538/PSRP-EASL2018.0001","DOIUrl":"https://doi.org/10.30538/PSRP-EASL2018.0001","url":null,"abstract":"A carbon nanotube (CNT) is a miniature cylindrical carbon structure that has hexagonal graphite molecules attached at the edges. In this paper, we compute the numerical invariant (Topological indices) of linear [n]-phenylenic, lattice of C4C6C8[m,n], TUC4C6C8[m,n] nanotube, C4C6C8[m,n] nanotori.","PeriodicalId":11518,"journal":{"name":"Engineering and Applied Science Letters","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2018-09-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44624177","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2018-06-27DOI: 10.30538/PSRP-EASL2018.0002
K. Nantomah
In this paper, we study completete monotonicity properties of the function $f_{a,k}(x)=psi^{(k)}(x+a) - psi^{(k)}(x) - frac{ak!}{x^{k+1}}$, where $ain(0,1)$ and $kin mathbb{N}_0$. Specifically, we consider the cases for $kin { 2n: nin mathbb{N}_0 }$ and $kin { 2n+1: nin mathbb{N}_0 }$. Subsequently, we deduce some inequalities involving the polygamma functions.
{"title":"Complete Monotonicity Properties of a Function Involving the Polygamma Function","authors":"K. Nantomah","doi":"10.30538/PSRP-EASL2018.0002","DOIUrl":"https://doi.org/10.30538/PSRP-EASL2018.0002","url":null,"abstract":"In this paper, we study completete monotonicity properties of the function $f_{a,k}(x)=psi^{(k)}(x+a) - psi^{(k)}(x) - frac{ak!}{x^{k+1}}$, where $ain(0,1)$ and $kin mathbb{N}_0$. Specifically, we consider the cases for $kin { 2n: nin mathbb{N}_0 }$ and $kin { 2n+1: nin mathbb{N}_0 }$. Subsequently, we deduce some inequalities involving the polygamma functions.","PeriodicalId":11518,"journal":{"name":"Engineering and Applied Science Letters","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2018-06-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46207042","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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