Some results on semi-total signed graphs

Deepa Sinha; Pravin Garg

Displaying similar documents to “Some results on semi-total signed graphs”

On $(n, m)$ - $A$ -normal and $(n, m)$ - $A$ -quasinormal semi-Hilbertian space operators

Samir Al Mohammady, Sid Ahmed Ould Beinane, Sid Ahmed Ould Ahmed Mahmoud (2022)

Mathematica Bohemica

Similarity:

The purpose of the paper is to introduce and study a new class of operators on semi-Hilbertian spaces, i.e. spaces generated by positive semi-definite sesquilinear forms. Let $ℋ$ be a Hilbert space and let $A$ be a positive bounded operator on $ℋ$ . The semi-inner product ${〈 h ∣ k 〉}_{A} : = 〈 A h ∣ k 〉$ , $h, k \in ℋ$ , induces a semi-norm ${∥ \cdot ∥}_{A}$ . This makes $ℋ$ into a semi-Hilbertian space. An operator $T \in ℬ_{A} (ℋ)$ is said to be $(n, m)$ - $A$ -normal if $[T^{n}, {(T^{♯_{A}})}^{m}] : = T^{n} {(T^{♯_{A}})}^{m} - {(T^{♯_{A}})}^{m} T^{n} = 0$ for some positive integers $n$ and $m$ .

Degree sums of adjacent vertices for traceability of claw-free graphs

Tao Tian, Liming Xiong, Zhi-Hong Chen, Shipeng Wang (2022)

Czechoslovak Mathematical Journal

Similarity:

The line graph of a graph $G$ , denoted by $L (G)$ , has $E (G)$ as its vertex set, where two vertices in $L (G)$ are adjacent if and only if the corresponding edges in $G$ have a vertex in common. For a graph $H$ , define ${\bar{σ}}_{2} (H) = min {d (u) + d (v) : u v \in E (H)}$ . Let $H$ be a 2-connected claw-free simple graph of order $n$ with $δ (H) \geq 3$ . We show that, if ${\bar{σ}}_{2} (H) \geq \frac{1}{7} (2 n - 5)$ and $n$ is sufficiently large, then either $H$ is traceable or the Ryjáček’s closure $cl (H) = L (G)$ , where $G$ is an essentially $2$ -edge-connected triangle-free graph that can be contracted to one of the two graphs of order 10...

Migrativity properties of 2-uninorms over semi-t-operators

Ying Li-Jun, Qin Feng (2022)

Kybernetika

Similarity:

In this paper, we analyze and characterize all solutions about $α$ -migrativity properties of the five subclasses of 2-uninorms, i. e. $C^{k}$ , $C_{k}^{0}$ , $C_{k}^{1}$ , $C_{1}^{0}$ , $C_{0}^{1}$ , over semi-t-operators. We give the sufficient and necessary conditions that make these $α$ -migrativity equations hold for all possible combinations of 2-uninorms over semi-t-operators. The results obtained show that for $G \in C^{k}$ , the $α$ -migrativity of $G$ over a semi-t-operator $F_{μ, ν}$ is closely related to the $α$ -section of $F_{μ, ν}$ or the ordinal sum representation...

On sets of discontinuities of functions continuous on all lines

Luděk Zajíček (2022)

Commentationes Mathematicae Universitatis Carolinae

Similarity:

Answering a question asked by K. C. Ciesielski and T. Glatzer in 2013, we construct a $C^{1}$ -smooth function $f$ on $[0, 1]$ and a closed set $M \subset graph f$ nowhere dense in $graph f$ such that there does not exist any linearly continuous function on $ℝ^{2}$ (i.e., function continuous on all lines) which is discontinuous at each point of $M$ . We substantially use a recent full characterization of sets of discontinuity points of linearly continuous functions on $ℝ^{n}$ proved by T. Banakh and O. Maslyuchenko in 2020. As an easy consequence...

Some results on semi-stratifiable spaces

Wei-Feng Xuan, Yan-Kui Song (2019)

Mathematica Bohemica

Similarity:

We study relationships between separability with other properties in semi-stratifiable spaces. Especially, we prove the following statements: (1) If $X$ is a semi-stratifiable space, then $X$ is separable if and only if $X$ is $D C (ω_{1})$ ; (2) If $X$ is a star countable extent semi-stratifiable space and has a dense metrizable subspace, then $X$ is separable; (3) Let $X$ be a $ω$ -monolithic star countable extent semi-stratifiable space. If $t (X) = ω$ and $d (X) \leq ω_{1}$ , then $X$ is hereditarily separable. Finally, we prove that for...

Characterization by intersection graph of some families of finite nonsimple groups

Hossein Shahsavari, Behrooz Khosravi (2021)

Czechoslovak Mathematical Journal

Similarity:

For a finite group $G$ , $Γ (G)$ , the intersection graph of $G$ , is a simple graph whose vertices are all nontrivial proper subgroups of $G$ and two distinct vertices $H$ and $K$ are adjacent when $H \cap K \neq 1$ . In this paper, we classify all finite nonsimple groups whose intersection graphs have a leaf and also we discuss the characterizability of them using their intersection graphs.

Even factor of bridgeless graphs containing two specified edges

Nastaran Haghparast, Dariush Kiani (2018)

Czechoslovak Mathematical Journal

Similarity:

An even factor of a graph is a spanning subgraph in which each vertex has a positive even degree. Let $G$ be a bridgeless simple graph with minimum degree at least $3$ . Jackson and Yoshimoto (2007) showed that $G$ has an even factor containing two arbitrary prescribed edges. They also proved that $G$ has an even factor in which each component has order at least four. Moreover, Xiong, Lu and Han (2009) showed that for each pair of edges $e_{1}$ and $e_{2}$ of $G$ , there is an even factor containing $e_{1}$ and $e_{2}$ ...

Saturation numbers for linear forests $P_{6} + t P_{2}$

Jingru Yan (2023)

Czechoslovak Mathematical Journal

Similarity:

A graph $G$ is $H$ -saturated if it contains no $H$ as a subgraph, but does contain $H$ after the addition of any edge in the complement of $G$ . The saturation number, $sat (n, H)$ , is the minimum number of edges of a graph in the set of all $H$ -saturated graphs of order $n$ . We determine the saturation number $sat (n, P_{6} + t P_{2})$ for $n \geq \frac{10}{3} t + 10$ and characterize the extremal graphs for $n > \frac{10}{3} t + 20$ .

Edge-colouring of graphs and hereditary graph properties

Samantha Dorfling, Tomáš Vetrík (2016)

Czechoslovak Mathematical Journal

Similarity:

Edge-colourings of graphs have been studied for decades. We study edge-colourings with respect to hereditary graph properties. For a graph $G$ , a hereditary graph property $𝒫$ and $l \geq 1$ we define $χ_{𝒫, l}^{'} (G)$ to be the minimum number of colours needed to properly colour the edges of $G$ , such that any subgraph of $G$ induced by edges coloured by (at most) $l$ colours is in $𝒫$ . We present a necessary and sufficient condition for the existence of $χ_{𝒫, l}^{'} (G)$ . We focus on edge-colourings of graphs with respect to the hereditary...

Some results on the co-intersection graph of submodules of a module

Lotf Ali Mahdavi, Yahya Talebi (2018)

Commentationes Mathematicae Universitatis Carolinae

Similarity:

Let $R$ be a ring with identity and $M$ be a unitary left $R$ -module. The co-intersection graph of proper submodules of $M$ , denoted by $Ω (M)$ , is an undirected simple graph whose vertex set $V (Ω)$ is a set of all nontrivial submodules of $M$ and two distinct vertices $N$ and $K$ are adjacent if and only if $N + K \neq M$ . We study the connectivity, the core and the clique number of $Ω (M)$ . Also, we provide some conditions on the module $M$ , under which the clique number of $Ω (M)$ is infinite and $Ω (M)$ is a planar graph. Moreover, we give...

On the intersection graph of a finite group

Hossein Shahsavari, Behrooz Khosravi (2017)

Czechoslovak Mathematical Journal

Similarity:

For a finite group $G$ , the intersection graph of $G$ which is denoted by $Γ (G)$ is an undirected graph such that its vertices are all nontrivial proper subgroups of $G$ and two distinct vertices $H$ and $K$ are adjacent when $H \cap K \neq 1$ . In this paper we classify all finite groups whose intersection graphs are regular. Also, we find some results on the intersection graphs of simple groups and finally we study the structure of $Aut (Γ (G))$ .

On the diameter of the intersection graph of a finite simple group

Xuanlong Ma (2016)

Czechoslovak Mathematical Journal

Similarity:

Let $G$ be a finite group. The intersection graph $Δ_{G}$ of $G$ is an undirected graph without loops and multiple edges defined as follows: the vertex set is the set of all proper nontrivial subgroups of $G$ , and two distinct vertices $X$ and $Y$ are adjacent if $X \cap Y \neq 1$ , where $1$ denotes the trivial subgroup of order $1$ . A question was posed by Shen (2010) whether the diameters of intersection graphs of finite non-abelian simple groups have an upper bound. We answer the question and show that the diameters...