61–80 of
114 results.

Maryam Atapour
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Seyyed Mahmoud Sheikholeslami
A nonnegative signed dominating function (NNSDF) of a graph $G$is a function $f$ from the vertex set $V(G)$ to the set $\{1,1\}$such that $\sum_{u\in N[v]}f(u)\ge 0$ for every vertex $v\inV(G)$. The ...

Ioan Tomescu
In this paper, we show that in the classof connected graphs $G$ of order $n\geq 3$ having girth at least equal to $k$, $3\leq k\leq n$, the unique graph $G$ having minimum general sumconnectivity ind...

Chandrashekar Adiga
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Rakshith B. R.
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K.N., Subba Krishna
In this paper we define extended corona and extended neighborhoodcorona of two graphs $G_{1}$ and $G_{2}$, which are denoted by$G_{1}\bullet G_{2}$ and $G_{1}\ast G_{2}$ respectively. Wecompute their ...

Sung Sik U.
This paper discusses the enumeration for rooted spanning trees and forests of the labelled join graphs $K_m+H_n$ and $K_m+K_{n,p}$, where $H_n$ is a graph with $n$ isolated vertices.

Michael Haythorpe
A constructive method is provided that outputs a directed graph which is named a broken crown graph, containing $5n9$ vertices and $k$ Hamiltonian cycles for any choice of integers $n \geq k \geq 4$....

Jeremy Moody
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P. K. Aravind
This paper shows how a method developed by Van Steenwijk can be generalized to calculate the resistance between any two vertices of a symmetrical polytope all of whose edges are identical resistors. T...

Christian Rubio Montiel
A graph $G$ is \emph{trivially perfect} if for every induced subgraph the cardinality of the largest set of pairwise nonadjacent vertices (the stability number) $\alpha(G)$ equals the number of (maxim...

Seyed Mahmoud Sheikholeslami
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Lutz Volkmann
Let $D$ be a finite and simple digraph with vertex set $V(D)$.A {\em signed Roman dominating function} on the digraph $D$ isa function $f:V (D)\longrightarrow \{1, 1, 2\}$ such that$\sum_{u\in N^[v...

Rafael Del Valle Vega
The BrualdiShen Conjecture on Eulerian Bipartite Tournaments states that any such graph can be decomposed into oriented 4cycles. In this article we prove the balanced case of the mentioned conjectur...

Gholam Hassan Shirdel
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Nasrin Kahkeshani
The purpose of the independent set interdiction problem in the weighted graph $G$ is to determine a set of vertices $R^*$ such that the weight of the maximum independent set in $GR^*$ is minimized. W...

Harishchandra S. Ramane
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Ashwini S. Yalnaik
The reciprocal complementary distance (RCD) matrix of a graph $G$ is defined as $RCD(G) = [rc_{ij}]$ where $rc_{ij} = \frac{1}{1+Dd_{ij}}$ if $i \neq j$ and $rc_{ij} = 0$, otherwise, where $D$ is the...

Jemal Abawajy
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Andrei Kelarev
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Joe Ryan
The present article continues the investigation of visible ideal bases in constructions defined using directed graphs. This notion is motivated by its applications for the design of classication syste...

P. Anusha Devi
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S. Monikandan
An ecard of a graph $G$ is a subgraph formed by deleting an edge. A daecard specifies the degree of the deleted edge along with the ecard. The degree associated edge reconstruction number of a graph ...

Antoon H. Boode
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Hajo Broersma
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Jan F. Broenink
In this paper we introduce and study a directed tree problem motivated by a new graph product that we have recently introduced and analysed in two conference contributions in the context of periodic r...

Shariefuddin Pirzada
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Muhammad Ali Khan
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Zhou Guofei
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Koko K. Kayibi
A $k$hypertournament is a complete $k$hypergraph with each $k$edge endowed with an orientation, that is, a linear arrangement of the vertices contained in the edge. In a $k$hypertournament, the sc...

Xueliang Li
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Yongtang Shi
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Martin Trinks
The matching polynomial of a graph is the generating function of the numbers of its matchings with respect to their cardinality. A graph polynomial is polynomial reconstructible, if its value for a gr...

Hilal A. Ganie
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Shariefuddin Pirzada
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Edy Tri Baskoro
For a graph $G$ having adjacency spectrum ($A$spectrum) $\lambda_n\leq\lambda_{n1}\leq\cdots\leq\lambda_1$ and Laplacian spectrum ($L$spectrum) $0=\mu_n\leq\mu_{n1}\leq\cdots\leq\mu_1$, the energy...

Salman Ghazal
Seymour's second neighborhood conjecture states that every simple digraph (without digons) has a vertex whose first outneighborhood is at most as large as its second outneighborhood. Such a vertex i...

Sudev Naduvath
A setlabeling of a graph $G$ is an injective function $f:V(G)\to \mathcal{P}(X)$, where $X$ is a finite set and a setindexer of $G$ is a setlabeling such that the induced function $f^{\oplus}:E(G)...

Jonathan L. Gross
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Toufik Mansour
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Thomas W. Tucker
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David G. L. Wang
A Ringel ladder can be formed by a selfbaramalgamation operation on a symmetric ladder, that is, by joining the root vertices on its endrungs. The present authors have previously derived criteria u...