1–20 of
129 results.

Fendy Septyanto
•
Kiki A. Sugeng
Let G be a graph with an edge kcoloring γ : E(G) → {1, …, k} (not necessarily proper). A path is called a rainbow path if all of its edges have different colors. The map γ is called a rainbow colorin...

Ebrahim Vatandoost
•
Masoumeh Khalili
Let G be a nonabelian group. The noncommuting graph of group G, shown by ΓG, is a graph with the vertex set G \ Z(G), where Z(G) is the center of group G. Also two distinct vertices of a and b are a...

Hafizh M. Radiapradana
•
Suhadi Wido Saputro
•
Erma Suwastika
•
Oki Neswan
•
Andrea SemanicovaFenovcıkova
For integer k ≥ 2, let X = {0, 1, 2, …, k}. In this paper, we determine the order of a star graph K1, n of n + 1 vertices, such that K1, n admits a topological integer additive setlabeling (TIASL) wi...

Christina EubanksTurner
•
Aihua Li
In this paper, we study the interlace polynomials of friendship graphs, that is, graphs that satisfy the Friendship Theorem given by Erdös, Rényi and Sos. Explicit formulas, special values and behavio...

Salman Ghazal
We find the structure of graphs that have no C4, $\overline{C}_4$, C5, S3, chair and cochair as induced subgraphs. Then we deduce the structure of the graphs having no induced C4, $\overline{C_4}$, S...

SarahMarie Belcastro
We correct a small error in a 1996 paper of Albertson and Haas, and extend their lower bound for the fraction of properly colorable edges of planar subcubic graphs that are simple, connected, bridgele...

Cristina Dalfo
•
Miquel Àngel Fiol
A graph is a mathematical object modeling the existence of a certain relation between pairs of elements of a given set. Many of the first results concerning graphs made reference to relationships betw...

Diamantis Koreas
V.G. Vizing showed that any graph belongs to one of two classes: Class 1 if χʹ(G) = Δ(G) or in class 2 if χʹ(G) = Δ(G) + 1, where χʹ(G) and Δ(G) denote the edge chromatic index of G and the maximum de...

Leomarich F. Casinillo
Let G = (V(G), E(G)) be a path of order n ≥ 1. Let fm(G) be a path with m ≥ 0 independent dominating vertices which follows a Fibonacci string of binary numbers where 1 is the dominating vertex. A set...

Chithra Mr
•
Manju K. Menon
•
A. Vijayakumar
Many graphs such as hypercubes, star graphs, pancake graphs, grid, torus etc are known to be good interconnection network topologies. In any network topology, the vertices represent the processors and...

Abdollah Alhevaz
•
Maryam Baghipur
•
Ebrahim Hashemi
The distance signless Laplacian spectral radius of a connected graph G is the largest eigenvalue of the distance signless Laplacian matrix of G, defined as DQ(G) = Tr(G) + D(G), where D(G) is th...

S. Susilawati
•
Edy Tri Baskoro
•
Rinovia Simanjuntak
In 2010, Nurdin, Baskoro, Salman and Gaos conjectured that the total vertex irregularity strength of any tree T is determined only by the number of vertices of degrees 1, 2 and 3 in T. This paper will...

Dalibor Froncek
•
Aaron Shepanik
A handicap distance antimagic labeling of a graph G = (V, E) with n vertices is a bijection f̂ : V → {1, 2, …, n} with the property that f̂(xi) = i, the weight w(xi) is the sum of labels of all neighb...

Ju Zhou
A graph G is perfect matching transitive, shortly PMtransitive, if for any two perfect matchings M and N of G, there is an automorphism f : V(G) ↦ V(G) such that fe(M) = N, where fe(uv) = f(u)f(v). I...

Håkan Lennerstad
•
Mattias Eriksson
In this paper we consider node labelings c of an undirected connected graph G=(V,E) with labels {1,2,... ,V}, which induce a list distance c(u,v)=c(v)c(u) besides the usual graph distance d(u,v)....

Marvin Minei
•
Howard Skogman
We give a new construction of Ramanujan graphs using a generalized type of covering graph called a weighted covering graph. For a given prime p the basic construction produces bipartite Ramanujan grap...

Luis R. Fuentes
•
Italo J. Dejter
•
Carlos A. Araujo
Let $0<n\in\mathbb{Z}$. In the unit distance graph of $\mathbb{Z}^n\subset\mathbb{R}^n$, a perfect dominating set is understood as having induced components not necessarily trivial. A modification ...

Nobuaki Obata
•
Alfi Y. Zakiyyah
A connected graph is said to be of QE class if it admits a quadratic embedding in a Hilbert space, or equivalently, if the distance matrix is conditionally negative definite. Several criteria for a g...

Ramin Nasiri
•
Hamid Reza Ellahi
•
Gholam Hossein FathTabar
•
Ahmad Gholami
The signless Laplacian Estrada index of a graph $G$ is defined as $SLEE(G)=\sum^{n}_{i=1}e^{q_i}$ where $q_1, q_2, \ldots, q_n$ are the eigenvalues of the signless Laplacian matrix of G. Following th...

Vladimir Dimitrov Samodivkin
The bondage number b(G) of a graph G is the smallest number of edges whose removal from G results in a graph with larger domination number. We obtain sufficient conditions for the validity of the ineq...