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Entropy Measures of Distance Matrix 距离矩阵的熵测度
IF 0.8
Discrete Mathematics Letters Pub Date : 2021-11-08 DOI: 10.20944/preprints202111.0145.v1
B. Şahin, A. Şahin
{"title":"Entropy Measures of Distance Matrix","authors":"B. Şahin, A. Şahin","doi":"10.20944/preprints202111.0145.v1","DOIUrl":"https://doi.org/10.20944/preprints202111.0145.v1","url":null,"abstract":"Bonchev and Trinajstic defined two distance based entropy measures to measure the molecular branching of molecular graphs in 1977 [Information theory, distance matrix, and molecular branching, J. Chem. Phys., 38 (1977), 4517–4533]. In this paper we use these entropy measures which are based on distance matrices of graphs. The first one is based on distribution of distances in distance matrix and the second one is based on distribution of distances in upper triangular submatrix. We obtain the two entropy measures of paths, stars, complete graphs, cycles and complete bipartite graphs. Finally we obtain the minimal trees with respect to these entropy measures with fixed diameter.","PeriodicalId":36023,"journal":{"name":"Discrete Mathematics Letters","volume":" ","pages":""},"PeriodicalIF":0.8,"publicationDate":"2021-11-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43752701","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}
引用次数: 0
A Note on Rainbow Mean Indexes of Paths 关于路径的彩虹平均指数的一个注记
IF 0.8
Discrete Mathematics Letters Pub Date : 2021-10-29 DOI: 10.47443/dml.2021.0099
{"title":"A Note on Rainbow Mean Indexes of Paths","authors":"","doi":"10.47443/dml.2021.0099","DOIUrl":"https://doi.org/10.47443/dml.2021.0099","url":null,"abstract":"","PeriodicalId":36023,"journal":{"name":"Discrete Mathematics Letters","volume":" ","pages":""},"PeriodicalIF":0.8,"publicationDate":"2021-10-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43971073","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}
引用次数: 0
Periodical Burst Error Correcting Codes With Decoding Error Probability 具有译码错误概率的周期性突发纠错码
IF 0.8
Discrete Mathematics Letters Pub Date : 2021-10-27 DOI: 10.47443/dml.2021.0077
P. Das, Letminthang Haokip
{"title":"Periodical Burst Error Correcting Codes With Decoding Error Probability","authors":"P. Das, Letminthang Haokip","doi":"10.47443/dml.2021.0077","DOIUrl":"https://doi.org/10.47443/dml.2021.0077","url":null,"abstract":"Error control codes are used to control the effect of transmission or channel errors. Identifying the channel errors and applying the corresponding error control code can avoid the correction of unwarranted errors, thus improving the efficiency of the communication system. In [12], Lange introduces a type of channel error (disturbance) called periodical burst error which is found in data transmission via power lines, data channels in close distance to electronically controlled power supply units or inverters, car electric, compact discs and CD-ROM. The periodical burst error can be defined as follows.","PeriodicalId":36023,"journal":{"name":"Discrete Mathematics Letters","volume":" ","pages":""},"PeriodicalIF":0.8,"publicationDate":"2021-10-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42774667","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}
引用次数: 1
Some Combinatorial Identities Concerning Harmonic Numbers and Binomial Coefficients 关于调和数和二项式系数的一些组合恒等式
IF 0.8
Discrete Mathematics Letters Pub Date : 2021-10-25 DOI: 10.47443/dml.2021.0090
Dongwei Guo
{"title":"Some Combinatorial Identities Concerning Harmonic Numbers and Binomial Coefficients","authors":"Dongwei Guo","doi":"10.47443/dml.2021.0090","DOIUrl":"https://doi.org/10.47443/dml.2021.0090","url":null,"abstract":"School of Mathematics and Statistics, Zhoukou Normal University, Henan, China (Received: 6 September 2021. Received in revised form: 8 October 2021. Accepted: 21 October 2021. Published online: 25 October 2021.) c © 2021 the author. This is an open access article under the CC BY (International 4.0) license (www.creativecommons.org/licenses/by/4.0/). Abstract An elementary proof for a binomial identity of Batir [Integers 20 (2020) #A25] is presented and several combinatorial identities concerning harmonic numbers and binomial coefficients are derived.","PeriodicalId":36023,"journal":{"name":"Discrete Mathematics Letters","volume":" ","pages":""},"PeriodicalIF":0.8,"publicationDate":"2021-10-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44471258","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}
引用次数: 2
Non-semiregular bipartite graphs with integer Sombor index 具有整数Sombor指数的非半正则二部图
IF 0.8
Discrete Mathematics Letters Pub Date : 2021-10-23 DOI: 10.47443/dml.2021.0107
M. Oboudi
{"title":"Non-semiregular bipartite graphs with integer Sombor index","authors":"M. Oboudi","doi":"10.47443/dml.2021.0107","DOIUrl":"https://doi.org/10.47443/dml.2021.0107","url":null,"abstract":"Abstract For a simple graphG, the Sombor index (a recently introduced vertex-degree based molecular structure descriptor) is defined as SO(G) = ∑ uv∈E(G) √ du + dv, where dv is the degree of v. A graph is bipartite semi-regular if it is bipartite bidegreed and all vertices in the same class of bipartition have the same degree. In the recent paper [T. Došlić, T. Réti, A. Ali, Discrete Math. Lett. 7 (2021) 1–4] the following claim was posed: “Let G be a connected bipartite graph. Then SO(G) is an integer if and only if G is bipartite semi-regular and its degrees δ and ∆ appear as non-maximal elements in some Pythagorean triple”. In the present paper we show that the ‘only if’ part of the mentioned claim is not true. More precisely, we construct infinite number of connected bipartite graphs such that in their degree sequences there are three or four distinct numbers.","PeriodicalId":36023,"journal":{"name":"Discrete Mathematics Letters","volume":" ","pages":""},"PeriodicalIF":0.8,"publicationDate":"2021-10-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44633486","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}
引用次数: 2
Binomial Tribonacci Sums 二项式Tribonacci和
IF 0.8
Discrete Mathematics Letters Pub Date : 2021-10-13 DOI: 10.47443/dml.2021.0080
K. Adegoke, R. Frontczak, T. Goy
{"title":"Binomial Tribonacci Sums","authors":"K. Adegoke, R. Frontczak, T. Goy","doi":"10.47443/dml.2021.0080","DOIUrl":"https://doi.org/10.47443/dml.2021.0080","url":null,"abstract":"Abstract We derive expressions for several binomials sums involving a generalized tribonacci sequence. We also study double binomial sums involving this sequence. Several explicit examples involving tribonacci and tribonacci–Lucas numbers are stated to highlight the results.","PeriodicalId":36023,"journal":{"name":"Discrete Mathematics Letters","volume":" ","pages":""},"PeriodicalIF":0.8,"publicationDate":"2021-10-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48422534","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}
引用次数: 1
Mean Sombor Index 平均忧郁指数
IF 0.8
Discrete Mathematics Letters Pub Date : 2021-10-06 DOI: 10.47443/dml.2021.s204
J. A. M´endez-Berm´udez, R. Aguilar-S´anchez, Edil D. Molina, Jos´e M. Rodr´ıguez, Carlos E. Adame, Col. Garita, Acapulco Gro, Mexico 39650
{"title":"Mean Sombor Index","authors":"J. A. M´endez-Berm´udez, R. Aguilar-S´anchez, Edil D. Molina, Jos´e M. Rodr´ıguez, Carlos E. Adame, Col. Garita, Acapulco Gro, Mexico 39650","doi":"10.47443/dml.2021.s204","DOIUrl":"https://doi.org/10.47443/dml.2021.s204","url":null,"abstract":"We introduce a degree-based variable topological index inspired on the power (or generalized) mean. We name this new index as the mean Sombor index: $mSO_alpha(G) = sum_{uv in E(G)} left[left( d_u^alpha+d_v^alpha right) /2 right]^{1/alpha}$. Here, $uv$ denotes the edge of the graph $G$ connecting the vertices $u$ and $v$, $d_u$ is the degree of the vertex $u$, and $alpha in mathbb{R} backslash {0}$. We also consider the limit cases $mSO_{alphato 0}(G)$ and $mSO_{alphatopminfty}(G)$. Indeed, for given values of $alpha$, the mean Sombor index is related to well-known topological indices such as the inverse sum indeg index, the reciprocal Randic index, the first Zagreb index, the Stolarsky--Puebla index and several Sombor indices. Moreover, through a quantitative structure property relationship (QSPR) analysis we show that $mSO_alpha(G)$ correlates well with several physicochemical properties of octane isomers. Some mathematical properties of mean Sombor indices as well as bounds and new relationships with known topological indices are also discussed.","PeriodicalId":36023,"journal":{"name":"Discrete Mathematics Letters","volume":" ","pages":""},"PeriodicalIF":0.8,"publicationDate":"2021-10-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49018228","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}
引用次数: 3
A note on the identification numbers of caterpillars 关于毛毛虫识别号的一点注记
IF 0.8
Discrete Mathematics Letters Pub Date : 2021-09-23 DOI: 10.47443/dml.2021.0073
Yuya Kono, Ping Zhang
{"title":"A note on the identification numbers of caterpillars","authors":"Yuya Kono, Ping Zhang","doi":"10.47443/dml.2021.0073","DOIUrl":"https://doi.org/10.47443/dml.2021.0073","url":null,"abstract":"A red-white coloring of a nontrivial connected graph G of diameter d is an assignment of red and white colors to the vertices of G where at least one vertex is colored red. Associated with each vertex v of G is a d-vector, called the code of v, whose ith coordinate is the number of red vertices at distance i from v. A red-white coloring of G for which distinct vertices have distinct codes is called an identification coloring or ID-coloring of G. A graph G possessing an ID-coloring is an ID-graph. The minimum number of red vertices among all ID-colorings of an ID-graph G is the identification number or ID-number of G. A caterpillar is a tree of order 3 or more, the removal of whose leaves produces a path. A caterpillar possessing an ID-coloring is an ID-caterpillar. In this note, we characterize all ID-caterpillars, determine all possible values of the ID-numbers of ID-caterpillars, and show that each value is realizable.","PeriodicalId":36023,"journal":{"name":"Discrete Mathematics Letters","volume":" ","pages":""},"PeriodicalIF":0.8,"publicationDate":"2021-09-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48167113","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}
引用次数: 1
Relating graph energy and Sombor index 关联图能量与Sombor指数
IF 0.8
Discrete Mathematics Letters Pub Date : 2021-09-23 DOI: 10.47443/dml.2021.0085
Alper Ülker, Arif Gürsoy, N. Gürsoy, I. Gutman
{"title":"Relating graph energy and Sombor index","authors":"Alper Ülker, Arif Gürsoy, N. Gürsoy, I. Gutman","doi":"10.47443/dml.2021.0085","DOIUrl":"https://doi.org/10.47443/dml.2021.0085","url":null,"abstract":"The energy of a graph (ε) is the sum of absolute values of its eigenvalues, thus it is a graph-spectrum-based quantity. The Sombor index (SO) is a recently conceived vertex-degree-based topological index. We establish various relations between ε and SO, among which are lower and upper bounds. These relations improve and extend earlier results communicated in the paper [A. Ülker, A. Gürsoy, N. K. Gürsoy, MATCH Commun. Math. Comput. Chem. 87 (2022) 51–58].","PeriodicalId":36023,"journal":{"name":"Discrete Mathematics Letters","volume":" ","pages":""},"PeriodicalIF":0.8,"publicationDate":"2021-09-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43882845","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}
引用次数: 5
Stolarsky–Puebla Index 斯托拉斯基-普埃布拉指数
IF 0.8
Discrete Mathematics Letters Pub Date : 2021-09-22 DOI: 10.47443/dml.2021.s203
J. A. Méndez-Bermúdez, R. Aguilar-Sánchez, R. Blaya, J. M. Sigarreta
{"title":"Stolarsky–Puebla Index","authors":"J. A. Méndez-Bermúdez, R. Aguilar-Sánchez, R. Blaya, J. M. Sigarreta","doi":"10.47443/dml.2021.s203","DOIUrl":"https://doi.org/10.47443/dml.2021.s203","url":null,"abstract":"We introduce a degree–based variable topological index inspired on the Stolarsky mean (known as the generalization of the logarithmic mean). We name this new index as the Stolarsky–Puebla index: SPα(G) = ∑ uv∈E(G) du, if du = dv, and SPα(G) = ∑ uv∈E(G) [(d α u − d α v ) / (α(du − dv)] , otherwise. Here, uv denotes the edge of the network G connecting the vertices u and v, du is the degree of the vertex u, and α ∈ R{0, 1}. Indeed, for given values of α, the Stolarsky– Puebla index reproduces well-known topological indices such as the reciprocal Randic index, the first Zagreb index, and several mean Sombor indices. Moreover, we apply these indices to random networks and demonstrate that 〈SPα(G)〉, normalized to the order of the network, scale with the corresponding average degree 〈d〉.","PeriodicalId":36023,"journal":{"name":"Discrete Mathematics Letters","volume":"1 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2021-09-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41364528","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}
引用次数: 2
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